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SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 21) Use implicit differentiation to determine the slope of the graph of √(x + y) = x at (2, 2). Enter just an integer. 22) Use implicit differentiation to determine the slope of the graph of x1/2.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Compute f(g(x)) for the given f(x) and g(x). 1) f(x) = (5/x - 7) and g(x) = (8/5x) A) (25x/8 - 35x) B) (25x/8 + 35x) C) (8x - 56/25x) D) (5x/8 - 35x) 2) f(x) = 4x2 and g(x) = (7/x) A).
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Differentiate. 1) y = 9x(4x2 - 3x) A) 108x2 - 27x B) 72x2 - 27x C) 108x2 - 54x D) 72x2 - 54x 2) y = (1 - 8x2)(6x2 - 192) A) -192x4 + 3084x2 B) -192x3 + 3084 C) 48x3 + 1542x D) -192x3 +.
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 41) Find the slope of the tangent line to f(x) = (x6 + 4x3 + 1/x3 + 1) at (1, f(1)). Enter just a reduced fraction of form (a/b). MULTIPLE CHOICE. Choose the one alternative that best.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) $1000 is invested at 6% interest compounded continuously. What is the value of the investment after 5 years? A) $1822.12 B) $1338.23 C) $6691.13 D) $1349.86 E) none of these 2) How long will it take for an investment to triple.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the area under the curve. 21) y = ex; x = -9 to x = 7 A) e7 - e9 B) e16 C) e7 - (1/e9) D) e7 + e9 22) Determine Δx formed by partitioning the given interval into n.
Suppose the position of an object moving in a straight line is given by the specified function. Find the instantaneous velocity at time t. 60) s(t) = t3 + 4t + 5, t = 1 A) 12 B) 7 C) 6 D) 10 Solve the problem. 61) A ball is thrown vertically upward from the ground at.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) What are the x-intercepts of the graph of y = 3x3 + 24? A) (24, 0) B) (0, 24) C) (2, 0) D) (0, -2) E) none of these Find the x-intercepts of the function. 2) f(x) = x2 + 4x -.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Find the derivative of f(x) = x5/2. A) (2/5)x-1/2 B) (5/2)x-1/2 C) 5x3/2 D) (5/2)x3/2 2) Find the derivative of f(x) = (1/(3)√(x)) A) (5/3x2) B) (2/3)x-4/3 C) - (1/3x4/3) D) none of these 3) Find the derivative of f(x) = 7x - 19 at.
Differentiate. 41) f(x) = (1/9)e9x A) e9x B) ex/9 C) (1/9)e9x D) 9e9x 42) f(x) = e2x^2 + x A) 4xe + 1 B) 4xex^2 + 1 C) 4xe2x^2 + 1 D) 4xe2x + 1 43) f(x) = e3 - 10x A) -10e3 - 10x B) -10ln(3 - 10x) C) e-10 D) 3e3 - 10x 44) f(x) = 8xex - 8ex A) 8xex + 16ex B) 8x C) 8ex D).
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Find the first derivative of w(t) = 7t2 - 19√(t) + 23 A) (7/2)t - (19/2)√(t) B) (7/2)t - (19/2√(t)) C) 14t - (19/2)√(t) D) 14t - (19/2√(t)) 2) Find the first derivative of y = T7 - 9T5 +.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 21) Which of the following is the equation of the line tangent to the curve y = √(x) at x = 9? (I) y = -x - (1/6) (II) y = (1/2)x + 3 (III) y = (1/6)x.
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 1) Is this the graph of a function having the following properties? (I) concave down for all x (II) asymptotic to the line x = 0 Enter your answer as just the word "yes" or the word "no".
Solve the problem. 19) Find the x coordinates of all relative extreme points of f(x) = (2/3)x3 - 7x2 + 24x - 72 A) x = -4, -3, 0 B) x = 3, 4 C) x = 2, 6 D) x = -4, -3 E) x = 0, 3, 4 20) Find the relative extreme points for.
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 41) A winter storm front moves through campus. At t hours after the onset of the storm, the temperature is given by T(t) = 35 - 2t2 + t. What is the average rate at.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 20) If 9t⋅34t⋅9-2t = √(3), find t. A) t = -2 B) t = (1/2) C) t = -1 D) t = (1/4) 21) If 5t + 5t + 5t = 75, find t. A) t = 5 B) t = 2 C) t.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Use the graph of f to determine if f is continuous at x = 2. A) no B) yes 2) Use the graph of f to determine if f is continuous at x = 2. A) yes B) no SHORT ANSWER..
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Estimate the slope of the curve y = ex at x = 0. A) e B) 1 C) ex D) 0 E) none of these SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 2).
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Determine if the function F is the general antiderivative of the function f. F(x) = 6x + (x3/2) + C; f(x) = 6 + 3x2 A) no B) yes 2) Determine if the function F is the general antiderivative.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) If e-x = 6, write x in terms of the natural logarithm. A) ln-6 B) ln6 C) -ln6 D) 6 2) If lnx = -3.6, write x using the exponential function. A) (1/e3.6) B) e3.6 C) (1/e-3.6) D) 3.6 Simplify. 3) ln(x2 - 2) + e⋅ln(x2.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Evaluate. 25) ∫(x7)dx A) 7x6 + C B) (1/7) x6 + C C) (1/8) x8 + C D) 8x8 + C 26) ∫(32)dx A) 16x2 + C B) 32x + C C) 0 D) 32 + C 27) ∫((7x2 - 4x))dx A) (7/3)x3 + C B) - (7/3)x3 -.
Compute the net change of the function. 24) Given f'(x) = 3x2 + 7, compute f(2) - f(-2). A) 4 B) -44 C) 0 D) 44 Refer to the figure to evaluate the definite integral. 25) Evaluate A) (57/2) B) (33/2) C) 33 D) (99/2) Solve the problem. 26) Suppose that f and g are continuous and that and A) 1 B) 21 C).
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 25) y = (4/3x3 + x2 + 4) Enter your answer as just: (P(x)/(Q(x))a) where P(x) and Q(x) are polynomials in standard form. 26) y = (1/√(2x + 1)) Enter your answer as just: (P(x)/(Q(x))a) where P(x) and.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine the growth constant k, then find all solutions of the differential equation. 1) y' = 0.4y A) k = 0.4, y = 0.4et B) k = 0.4, y = Ce0.4 C) k = 0.4, y = Cet D) k =.
Find the points of inflection. 37) f(x) = x3 - 3x2 + 2x + 15 A) (-1, -3) B) (1, -1) C) (1, -3) D) (1, 15) 38) f(x) = x3 + 12x2 - x - 24 A) (-4, 0) B) (-4, 132) C) (-4, 108) D) (4, 143) 39) f(x) = 2x3 + 3x2 - 12x A) (-2,32) B) (0, 0) C) (-.
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 21) f(x) = (1 + x2)ex Enter your answer exactly in the form (P(x))ea where P is a polynomial. 22) f(x) = (ex/1 + x2) Enter your answer exactly as ((P(x))ea/(Q(x))n) where P and Q are polynomials. MULTIPLE CHOICE..
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Write an equation of the tangent line to the graph of y = f(x) at the point on the graph where x has the indicated value. 20) f(x) = (4x2 - 5x - 2)(-2x - 3), x.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Compute the area of the shaded region. 1) A) 2 B) 16 C) 8 D) 32 2) A) 900 B) 30 C) 15 D) 45 3) A) (4/3) B) 1 C) (3/4) D) (1/3) 4) A) 40 -ln(1/ 9) B) 41 -ln(1/ 9) C) 40 -ln9 D) 80 -ln9 5) Given the graph of the function y.
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 21) Find the area of the region bounded by y = 6x - x2 and y = x2 - 2x. Enter a reduced fraction of form (a/b). 22) Find the area of the region bounded by y.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Simplify. 1) ln(x5y-4/w3z-2) A) 5lnx + 4lny - 3lnw - 2lnz B) 5lnx + 4lny - 3lnw + 2lnz C) 5lnx - 4lny - 3lnw - 2lnz D) 5lnx - 4lny - 3lnw + 2lnz E) none of these 2) ln(x4 - 5/z3y4) A).
Simplify the expression. 24) ex^2 - 4 = 3 A) 2 ± √(ln3) B) ± (2 + √(ln3)) C) ± √(4 +ln3) D) none of these 25) 2lnx +ln(1/x) = 3 A) e3 B) 1 + e2 C) ± √(ln3) D) ln3 E) none of these 26) ln(x + 1) = 2 +lnx A) e2 - 1 B) (1/e2 - 1) C) e + 1 D).
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Determine the percentage rate of change of f(x) = e0.9x at x = 15 and x = 30. A) (f'(15)/f(15)) = 90%, (f'(30)/f(30)) = 90% B) (f'(15)/f(15)) = 17%, (f'(30)/f(30)) = 29% C) (f'(15)/f(15)) = 38%, (f'(30)/f(30)) =.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Which of the following graphs could represent a function with the following properties? I. f(x) > 0, for x < 0 II. f '(x) ≤ 0, for all x III. f '(0) = 0 A) B) C) D) none of these 2) Which.
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 41) Determine the average value of f(x) = x3 over the interval from x = 0 to x = 4. Enter an integer. 42) Determine the average value of f(x) = (1/x2) over the interval from x.
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 24) Assume that a culture of bacteria grows at a rate proportional to its size such that if 106 bacteria are present initially, then there are 2 × 106 bacteria present after 3 hours. Determine.
Calculate the following limit(s) if they exist. 41) (1/x3 - 1) + 1 Enter either a fraction, integer, or the words "does not exist" 42) (x/(x3 + 8)-1) Enter either a fraction, integer, or the words "does not exist". 43) (g(x)/f(x)) where f(x) = - (1/3) and g(x) = (2/3). Enter your answer as an integer,.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find dy/dx by implicit differentiation. 1) 7y2 - 5x2 = 1 A) (5x/7y) B) (5x/7) C) (5x2/14y) D) (10x + 1/14y) 2) (1/3)x3 - 3y2 = 7 A) (x2/6y) B) (6y/x2) C) (6y/x2 + 7) D) (x2/3y) 3) 2y - x + xy = 6 A) - (1.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Differentiate. 1) f(x) = 4x2 - 4x - 7 A) f'(x) = 8x2 - 4 B) f'(x) = 8x - 4 C) f'(x) = 4x - 4 D) f'(x) = 4x2 - 4 2) f(x) = 3x4 + 5x3 + 1 A) f'(x).
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 21) e(lnx)^2 Enter your answer exactly as e(lnA)^b(clnd/f). 22) (lnx)5 Enter your answer as (P(lnx)/Q(x))where P is a polynomial in lnx and Q is a polynomial in x. 23) f(x) = (lnx)4 Enter your answer as just (P(lnx)/Q(x))where P is.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Differentiate. 1) y = ln3x A) - (1/x) B) - (1/3x) C) (1/x) D) (1/3x) 2) y = ln(x - 9) A) (1/9 - x) B) (1/x - 9) C) - (1/x + 9) D) (1/x + 9) 3) y = ln8x2 A) (2x/x2 + 8) B) (2/x) C) (16/x) D).
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 21) Let f(x) = x3. Using the chain rule, find an expression for the derivative of [f(g(x))]. A) 3[g(x)]2 g'(x) B) 3x2 g'(x)3 C) g'(x)3 D) 3[g(x)]2 E) none of these 22) Let g(x) = √(x) . Using the chain rule, find.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Calculate. 1) A) ln3 B) (4/3) C) -e + ln3 D) -ln3 E) none of these 2) A) (1/2)(e2 - e-2) B) - (1/2)e-2x + C C) e2 - e2 D) (1/2)(e2 - e2) E) none of these 3) A) (1/3)e + (7/6) B) (1/3)e3 + (7/6) C) (1/3)e3.
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Simplify. 1) 4x⋅2x/2 Enter your answer exactly as 2b/c. 2) 2x⋅8x Enter your answer exactly as 2a. 3) (3x/6x)⋅8x⋅((32/4))x Enter your answer exactly as 2a. 4) 16x((1/8))x Enter your answer exactly as 2a. 5) (2-x^2)(x + 1)/x Enter your answer exactly in the form 2P(x).
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Set up an integral or sum of integrals and then find the area bounded by y = x2 + 3 and y = -5x - 3. A) = - (1/6) B) = - (149/6) C) = (1/6) D) =.
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 21) Compute (d2y/dy2)((9t2/3/2))|t = 8 Enter just a reduced fraction of form (a/b). 22) Let f(t) = t3 - (9/t). Compute (d2f/dt2)|t = 3 Enter just a fraction (a/b) in lowest terms. 23) Compute f ''(2) when f(t) =.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Compute the maximum product for two positive numbers with the property that the sum of the first plus five times the second is 5000. A) 600 B) 50,000 C) 25,000 D) 1,250,000 E) none of these 2) Compute the maximum product.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A manufacturer estimates that the profit from producing x units of a commodity is -x2 + 40x - 100 dollars per week. What is the maximum profit he can realize in one week? A) $400 B) $500 C).
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 55) Find the interval(s) where f is decreasing and concave up for f(x) = x3 - 3x2 - 24x + 3. Enter your answer in standard interval notation as either : (a, b) or (a, b)∪(c,d).
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Give an appropriate answer. 61) Letf(x) = -9 andg(x) = -6. Find[f(x) - g(x)]. A) -15 B) -9 C) -6 D) -3 62) Letf(x) = 8 andg(x) = -4. Find[f(x) ? g(x)]. A) -32 B) 4 C) -4 D) 6 63) Letf(x) = 8 andg(x) = 5..
Solve the problem. 18) A beverage company works out a demand function for its sale of soda and finds it to be q = D(x) = 3000 - 20x, where q = the quantity of sodas sold when the price per can, in cents, is x. At a price of 127 cents per.
