The Rolle's theorem is applicable for f(x) = cos x on [0, T]. True False A Moving to another question will save this response.

Q: Because f(t) = sin t and g(t) = tan t are odd functions, what can be said about the function h(t) =…

A: Given functions are: f(t) =  sin t g(t) = tan t Since we have, f(-t) = sin (-t) = - sin t = - f(t)…

Q: If f (x) = cos(3x), then f' (-) is equal to

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Q: It is known that the range of the function f(x)= a sinx+1 for xER is -2<f(x)≤4, then a = ?

A: Given fx=asin x+1,     ∀x∈ℝ range of fx is -2≤fx≤4

Q: Find f'(÷) for f(x) = 2 sin z cos x

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Q: If f(x) = 5 sin x + 12 cos z, then %3D f'(x) = f'(2) =

A: The question has been solved in detail in the next step.

Q: Let f(x) = cx + In(cos(x)). For what value of c is f'(T/4) = 5? %3D

A: Given: f(x)=cx+log(cos(x))  and f'π4=5 find values c

Q: Let  f(x) = cx + ln(cos(x)).  For what value of c is f'(pi/4)=4

A: sol:-    Given f(x) = (x+ln(cosx)  differentiating ω. r.t   x, we get    f1(x) = c+1cosx(-sin x)…

Q: Suppose f and f' are differentiable functions of r. Given f' () = 0, f" () -1, and g(x) = log…

A: Differentiate two times at given value

Q: Find constants c1 and c2 such that: F(x) = c1 sin(3x) + c2x cos(3x) is an antiderivative of f(x) =…

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Q: Let f(x) = (c + 1)x+ In(cos x). For what value of c is f'(/4)=6

A: This question can be solved using the concepts of differentiation.

Q: For f(x)=In(cos(x)), what is

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Q: calculate L4 for f(x)=76 cos(x/2) over [2pi/4, 2pi/2]

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Q: cos='A F'A where A =atib

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Q: is stricly increasing on (0, T /2). sin x Prove that the function f(x)=

A: Given that: f(x)=xsinx

Q: Determine if f is differentiable at x = 0 given that -1 4 cos if – 2 0, x # 1. (x – 1)6 '

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Q: Integrate the following function (with respect to x) using any available method. x cos 3x

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Q: Find the function that satisfies the given 4. f'(x) = 2 + cos x and f COS X = 1

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Q: Find the general antiderivative of f and check your answer by differentiating:   f (x) = 4x7 − 3 cos…

A: Given: fx=4x7-3cosx

Q: Differentiate f (x) = cos (In x) e“.

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Q: The following DE sin(x) +y cos(x) = 1 can be written as: dx Cos(x) sin(x) None of These 1-cos(x).…

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Q: Verify the formulas by differentiation.

A: To verify the formula ∫dxa2+x2=1atan-1xa+C using differentiation. We know that integration is…

Q: If f(x) = x² + cos(x), what is f" (x)?

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Q: Let f(x) = In(cos(x)). For what value of c is f'l =CX + TC 1? 4. C =

A: We can solve it for the value of c as below

Q: Find a and b which make the following function differentiable at x = 0; ax+b, x < 0 sin x, f(x) = =…

A: We know a function is differentiable if and only if Right hand derivative and left hand derivative…

Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (₹) < 0, ƒ (x) has a root in [o,]. If we…

A: In secant method the next approximation root may or may not lies in the previous two roots

Q: Find antiderivative of the following functions.  1. f(x)=sinx/(1+cos2x)  2. f(x)=x/(1+x4)

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Q: find the aradients of the functions below a)f(x, y) = e-3y cos4x

A: We have to find

Q: Find F'(x), f"(x) and f'"(x) for f(x)=x$+cos(9x).

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Q: Calculate L4 for f(x) = 24 cos () over %3D LA

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Q: Find the f( for this f (x) = l09, x Cos-lx

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Q: Find f(x), where f'(x) = sin(x) + cos(x) + 1 and f(T) = 2.

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Q: Let f(x) = cx + In(cos(x)). For what value of c is f'(n/4) = 9?

A: f (x) = cx + ln ( cosx)To Find: For what values of c is f' (π4) = 9Proof: We will differentiate f(x)…

Q: Find fxw- for the following function: f(x,y,z)=x² +cos(x² +z²)+sin(x³ + y)

A: Given: fx, y, z = x2 + cos x3+z2 + sin x3+y To find: The value of fxxyz

Q: E. If f(x) = sin x + In x, find f'(x). Check that your answer is reasonable by comparing the graphs…

A: f(x)= sin x+ ln x So, f'(x)= cos x +1/x

Q: Find for the following function. dx 3- cos X y = 4 + coS X

A: follow next styep

Q: Find f(x), where f'(x) = sin(x) + cos(x) +1 and f(T) = 2.

A: We have to find

Q: Given that (1 COS 4.r) x2 a, if x = 0 if x 0. J 16+ Vx -4 If f(x) is continuous at x = 0, find the…

A:

Q: 6. If f is continuous and f² f(x) dx = 6, evaluate S/² f (2 sin 0) cos de.

A: It is given that if f is continuous and ∫02f(x)dx =6 The objective is to evaluate ∫0π2f2Sin θcos θ…

Q: Let f(x) = cx + In(cos(x)). For what value of c is f' = 4? %3D 4 C =

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Q: Given that the function g(r) is defined on R by g(x): A a · sin(cos(1/a)) , if r +0 , if r = 0 What…

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Q: Let f(x) = cx + In(cos(x)). For what value of c is f'(" = 5? 4

A: Differentiate the given function w.r.t. x.…

Q: Find F'(x) given that F(x) 3+sin (5t) dt. |3D In (t8) Provide your answer below: F'(x) =

A: The objective is to find F'(x).

Q: Find the linearization of the following functions at x=0. a) sin x L(x)= x b) cos x L(x)= 1 c) tan x…

A: As per guideline we have to solve only three

Q: Find and b such that the following function is continuous at x=( [x] – 2a x 0 -

A: To find the values of a and b

Q: Let  f(x) = cx + ln(cos(x)).  For what value of c is  f '(π/4) = 9?

A: Consider the given function, fx=cx+lncosx first differentiate the function using chain rule as…

Q: In(x) Differentiate the function F(x) | cos(e') dt (for x>0). %3D 1/r Show and justify your work.

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Q: Find out the following Derivatives w.r. to x.   (i)       F(x)  =  (x+ 2)2           (iii) F(x) =…

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Q: Find a function f such that ∇f = ex cos yi − ex sin yj + zk.

A: Given, ∇f = ex cos yi − ex sin yj + zk.