Find the limit and the rate of convergence of lim_h rightarrow 0 e^h - (1 + h + 1/2 h^2)/h. Write a MATLAB code to compute e^h - (1 + h + 1/2 h^2)/h with h = 1/2, 1/2^2, ..., 1/2^10. (compare with your (theoretical) convergence rate and numerical results).
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Find the maximum and minimum values of f(x, y) = 6x + y on the ellipse x2 + 25y2 = 1 Find the dimensions of the rectangular box having the largest volume and surface area 176 square units. List the dimensions in ascending order:
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Find the local maximum and minimum values of f using both the First and Second Derivative Tests. (If an answer does not exist, enter DNE.) f(x) = x^5 - 5x + 1 local maximum value local minimum value Find the local maximum and minimum values of f using both the.
find the limit: lim t rightarrow sin2 at/bt2 where a and b are non zero constants. Find the limit: lim x rightarrow sinx/tanx Find the derivative of y = f(x) f(x) = sin2
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12.) Find the derivative of the following function y = 4 sin ^-1 2x^5
Solve for dy/dx = ?
(simplify do not factor)
13.) Find the derivative of the following function y = 0.4 tan ^-1 5x
Solve.
14. Which of the following forms would be best to use when trying to find a particular solution to the differential equation y'' + 5y? + 4y = (t^2 + 1)e^6t using the method of undetermined coefficients? The correct answer below is the form that contains all required terms for.
Find the relative extrema for y = x3 - 6x2 + 9x + 2 using the second derivative test. Local Maximum(s) occurs at x = Local Minimum(s) occurs at x = Find the absolute maximum and minimum: f(x) = 2 + 8x2 - x4, [-3, 1] Absolute Maximum occurs at.
11. Find the indefinite integral. cos 2x sin22 2xdx a. sin 2x 4-5 sin 2x+ 3 sin 2x +C b. sin 2x 5 sin 2x 3 sin 2x +C c. Sin 2x 2 3 sin 2x +C 5 sin 2x- 30 d. sin 2x 4-5 sin 2x+ 3 sin 2x.
15 feet ladder is leaning against a wall when the base starts to slide away. By the time the base is 12 feet from the house, the base is moving at the rate of 6 ft / sec. How fast is the top of the ladder sliding down the wall?.
1a) Show that the differential equation is exact and then find the implicit
solution of the diffferential equation.
(6xy-4xy+5x?)dx+(2x-4xy)dy=0
(1b) Check your solution by differentiating it implicitly
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Find the limit of the following function. Is the function continuous at the point being approached?
f(x)= \(lim_{X \rightarrow \pi/6} (csc^2x + 5\sqrt{3} \tan x)^\frac{1}{2}\)
Find the first and second derivatives of the following function.
y = \(2x^{-2}+\frac{2}{x}\)
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Find the limit (if it exists). (If an answer does not exist, write DNE and explain.) lim t --> 0+ of (3+e^(2t))i + [ (13e^(6t)?13)/9t ]j + e^(-9t)k . . . State the rule used to find the indicated limit and execute: lim t -->0+ of ((13e^6t-13)/9t) lim t--> 0+.
10-ft ladder is leaning against a house when its base starts to slide away. By the time the base is 8 ft from the house, the base is moving away at the rate of 6 ft/sec. What is the rate of change of the height of the top of the.
find the limit of the following sequence or state it diverges
Select the correct choice below and, if necessary, fill in the answer box to complete your choice (type an exact answer.) A. The sequence is monotonic, and it is bounded. It also converges, and the limit.
Find the limit, if it exists, or show that the limit does limit exits, you must prove it. lim_(x, y) rightarrow (0, 0) x^2y^2/x^2 + y^2 lim_(x, y) rightarrow (0, 0) xy/x^2 + y^2
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find the limit, if it exists, or show that the limit does not exist. \(\lim_{(x,y) \rightarrow (0,0)} xy^{2}-x^{3}/x^{2}+y^{2}\)
\(\lim_{x \rightarrow 0} x^{3}-x^{3}/x^{2}+x^{2}=\lim_{x \rightarrow 0} 0/2x^{2}\) and I dont know where to go from here.
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find the limit of f as (x,y) goes to (0,0) or show that the limit does not exist. consider converting the function to a polar coordinates to make finding the limit easier. f(x,y)= ((x-y)^4)/((x^2+y^2)^3/2) please show as much work as possible
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10.) Find the Laplace transform of the given function \(f(t) = 3t^{3}e^{9t}\)
What is the Laplace tranform of the above _________?
11.) Find the inverse transform of the given function \(F(s) = \frac{10}{7s - 8}\)
What is the inverse transform of.
Find the limit, if it exists, or type N if it does not exist. Compute the limit as (x,y) rightarrow (0,0) along the -axis for (x + 20y)2/x2 + 20 2 y2: Compute the limit as (x,y) rightarrow (0,0) along the y -axis for (x + 20y)2/x2 + 20 2.
Find the maximum rate of change of f(x,y,z)=x+y/z at the point (-4, 2, -4) and the direction in which it occurs. Maximum rate of change: = Direction (unit vector) in which it occurs: < , , >
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