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Question : 21) f(x) = (sinx^2/tanx) : 2163398

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

21) f(x) = (sinx^{2}/tanx)

Enter a quotient with cosine and sine functions last in their terms. No parentheses or labels or multiplication dots.

22) f(x) = ln(tanx) + tanx

Enter your answer exactly in the form a⋅(b + C) .

23) f(t) = tant^{6}

Enter your answer without parentheses, no labels.

24) f(t) = (sec3t)^{6}

Enter your answer without parentheses or labels, use a multiplication dot between the last two functions.

25) f(x) = secx^{2}

Enter your answer without parentheses or labels. Use the multiplication dot between the last two functions of x.

26) f(t) = csct^{-3}

Enter your answer without parentheses or labels. No multiplication dots. Enter your answer as a quotient leaving t^{-3} in that form.

27) f(t) = cot((1/t))

Enter just an unlabeled quotient of functions of t. No parentheses.

28) f(t) = (sec3t/tan5t)

Enter your answer without parentheses or labels. Enter a quotient of functions of t of form (a-b/C) using multiplication dots between all functions of t.

29) f(x) = sec√(x)

Enter your answer without parentheses, no labels, leave √(x) in your answer which should be entered as a quotient (ab/C) in terms of functions of √(x).

30) f(x) = csc^{3}x

Enter your answer without parentheses, no labels, use the multiplication dot between functions of x.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

31) Find the equation of the tangent line to the graph of f(x) = tanx at ((π/4), 1).

A) y = 2x + 1 - (π/2)

B) y = 2x - 1

C) y = 2x - (π/2)

D) y = 2x + (π/2)

E) none of these

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

32) Find the equation of the tangent line to the graph of y = ln(tanx) at x = (π/4).

Enter your answer in standard slope-intercept form with any quotients reduced with π in the numerator.

33) Find the slope of the tangent line to the graph of y = e^{tanx} at x = 0.

Enter just an integer.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Integrate.

34) ∫(e^{x}sec^{2}(e^{x})dx)

A) e^{x}tan(e^{x}) + C

B) (tan(e^{x})/e^{x}) + C

C) tan^{2}(e^{x}) + C

D) tan(e^{x}) + C

E) none of these

35) ∫(sec^{2}(1 - 2x)dx)

A) -2tan(1 - 2x) + C

B) 2tan(1 - 2x) + C

C) tan(1 - 2x) + C

D) - (1/2)tan(1 - 2x) + C

E) none of these

36)

A) (π/4)

B) (π/2)

C) (4/π)

D) - (π/4)

E) none of these

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

37) ∫(sec^{2} 5x)dx

Enter your answer without parentheses.

38) ∫(csc^{2}(3x + 1))dx

Enter your answer using parentheses around the argument of the function.

39) ∫((5/cos^{2}3x))dx

Enter your answer without parentheses.

40) dx

Enter just an integer.

41)

Enter just an integer.