间 Chapter 10.7, Problem 3E Find the limit. 3. lim (e-3ti+ · (e-³¹ ₁ + 1/7j+( 1-0 sin j+cos 2tk)

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A: We have to find derivative

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A: Given that f(x) = cos(e^x^(5sin(x))  To find the derivative of f(x)

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A: The antiderivative of a function f( x) is a function F(x), such as d/dx (F(x)) = f( x). The general…

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A: Given that: limx→0x4.cos23x

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A: Given,

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A: Solve the limit limx→01-cos2arcsinx1n1+x2

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A: The objective is to evaluate the integration

Q: cos(4x) cos(2x) sin(4x) sec(2x) 12. Verify: - sin(2x)

A: cos(2x ) =cos2(x)-sin2(x) = 2cos2(x)-1 =1-2sin2(x) sin(2x) = 2sin(x) cos(x)

Q: For the f(x) = 1/1-X^2 and g(x)= x^2/1-X^2 A) shows that these functions have the derivative B) what…

A: We need to find relation between f and g.

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Q: Identify which of the following functions require chain rule application to obtain their…

A: Chain rule is applicable for Composition of two functions only

Q: If f' is continuous, f(6) = 0, and f'(6) = 11, evaluate f(6+ 3x) + f(6 + 5x) lim Limit:

A: The objective is to evaluate the limit.

Q: (1) Compute f'(x), f"(x), and f(3 (x) if f(x) = 3x² – 5x + 7. -

A: Since, you have post the multiple question. I am answering the first one. Please post the question…

Q: What is the limit as t goes to 0 of    4 tan^-1(t)

A: Topic:- limit

Q: Find the limts of the following problems.  (a) an= tan^-1(3n/sqrt(9n^2+4))  (b) lim as n->…

A: (a). 4π​(b). 1Explanation:Step 1: Step 2:Step 3:

Q: f(x)=tan^-1(x) Use Taylor's theorem with error to give an estimat of tan^-1(1) = pi/4, without the…

A: f(t)=tan-1(t),  f(0)=0f'(t)=11+t2,   f'(0)=1f"(t)=-2t(1+t2)2,  p1(t)=f(0)+t f'(0)=tE1(t)=f"(c) t22!…

Q: Choose the correct graph of G(x) = } cos (x - 4): %3D 2 1 27 -1 -2

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Q: 10 - (*;")" 1/t 2' +3' f(t) = for t + 0. 3 lim f(t) =

A: The given function is ft=2t+3t31t  for t≠0. Find the limit value limt→+∞ft. Limit of the…