91. Let I, = | x" cos(x³) dx and J, = | x" sin(x²)dx. (a) Find a reduction formula that expresses I, in terms of Jp–2. Hint: Write x" cos(x²) as x"-'(x cos(x²)). (b) (c) Evaluate 13. Use the result of (a) to show that I, can be evaluated explicitly if n is odd.

Q: Differentiate the following functions using the quotient rule. a) You are given that f (x) a df dx…

A: The Power Rule:The Chain Rule:The Quotient Rule:

Q: Use the product rule to differentiate the function h, where a and b are real numbers. h(x) = e¯ax…

A: According to product rule, if f(x)=u(x)*v*x) then f’(x)=u(x)*v’(x)+v(x)*u(x).

Q: 2. If f(g(x)) = sin x + 3sinx - 1, determine possible expressions for f(x) and g(x), where g(x) # x.

A: (1st method/way): Let f(x)=x²+3x-1 and g(x)=sinx Then we can find f(g(x)) as follows…

Q: 5. Evaluate: 34 l vo dx dx. √9-16x2 0

A: To find the value of given integral.

Q: Differentiate the following functions. Simplify and factor your answer where possible. a) f(x) = e2x…

A:

Q: ution t= tan 2 tan). os(x)

A: We have to choose the correct answer from the given option

Q: Find all xE[0,2pi] that satisfy sin 2x + cos x = 0 x =

A: Topic- Trigonometric Equations We are given, sin(2x)+cos(x)=0 and x∈[0,2π] We know that sin(2x)=2sin…

Q: 1. Differentiate. a) f(x) = x43x b) g(x) = x² — e√x -

A: We need to perform differentiation.

Q: 1. Differentiate. Do not simplify. а. f(0) = 3cos(0*)sin(0³ – 2) b. f(x) = 4x + 25-x² + 2x-1

A:

Q: a) f(x) = 1+ Sinx b) f(x) = x² + 2x- 1 c) f(x) = 2* + 2 for all x eR for all x eR for all x eR

A: Given function are: [1] f(x) = 1 + Sinx   for all x ∈R [2] f(x) = x2 + 2x - 1  for all x ∈R [3] f(x)…

Q: 3. Determine the exact value of f"(0) for f(x) = (cos5x + 5x²)*.

A: Given

Q: 6. Find : (a) y = (x³ +5) tan 7x, %3D

A: