1. Determine if g is differentiable at r 0 if 2 cos r, if -1

Q: Let f(x) = cos x. We can compute f")(x) as follows: First, express 4m +r where m is a whole number…

A: Given, f(x) = cosx, we have to compute fn(x) according to the given information. First express n =…

Q: Refer to the figure to determine f'(a) for a = 1, 2, 6, 8. y 5- 4 3+ 2- 1- 1 2 3 4 5 6 7 8 9 (Give…

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Q: Evaluate f x'V 1+4x² dx.

A: Consider the definite integral ∫01x21+4x2 dx to evaluate this, first evaluate the indefinite…

Q: Q6. Verify 02 f exDy Dyx for the function f(x, y) = x² sin2y + y²sin2x

A: A detailed solution is given below.

Q: Q1/: a: Using the relation showthat Jv2 (x) =, cos x

A: See the attachment

Q: Q1/: a: Using the relation showthat J-va (x) = 2 cos x

A: We have to solve given problem:

Q: Which hyperbolic functions are increasing on their domains? A. tanh x and cosh x are increasing on…

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Q: Let f(r) = In r Find and simplify f"(x).

A: Please refer the attached image for complete solution. THANK YOU.

Q: Q2/Show that the functions is harmonic u = 2 x (1 - y)

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Q: For what numbers 0 is f(0) = csc 0 not defined?

A: To find the numbers θ where fθ=cscθ is not defined. Solution: We know that, cscθ=1sinθ A rational…

Q: Let f : R → R be a twice differentiable function such that f" + f = 0. Prove there exist constants…

A: Introduction: In mathematics, differentiation is the process of determining the derivative, or rate…

Q: Find F as a function of x and evaluate it at x = 0, x = /3, and x = = Tt/2. F(x) 6 de

A: We will use basic formula of Integration for first one and from second part just Value of the…

Q: (-) = { 2*. x 2 Find the values of a and b so that f will be differentiable at x = 2.

A: Given function is fx=7x2        ,x≤2ax+b    ,x>2. By continuity, 722=a2+b74=2a+b2a+b=28     ...1…

Q: Prove the identity. Work on one side only. cos(4x) = 18 sin² x+8 sin ¹ x

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Q: Which graph corresponds to the function given? h(x) = {x², x 1

A: Here we have to draw the graph of the function.

Q: Find the -of the following function : ду w = cos (x2 + 2 y) – e4x- z*y + y3 .A a w = 2 sin ( x2 + 2…

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Q: LO KB allla the domain of f (x) = x²-4 is: x-1 [-2, 1) U [2, 00) O (-0, -2] U [2, 0)O [-2, 1) O [2,…

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

A: Given

Q: one of the following pairs of functions are orthogonal on interval [-1, 1] Select one: x.cosx b. x,X…

A: Given the interval [-π,π] and the pair of function. a. x2,cosxb. x,x c. sinx,xd. NOTe. sinx,cosx We…

Q: Sketch: f(x) = [x + 2]] − 1, on [−2,2]

A: We have to draw the graph

Q: 8. Consider the functions f : (4, 0) → R where f(x) = sin x and g : (-12,3) → R where g(x) = |x +…

A: Solution

Q: a) Let n be a postive integer. In this part a) you will prove the Power = V¤ = x² on (0, 0). Rule…

A: Formula used:

Q: etermine if g is differentiable at x = 0 if -1 COS if – 1 0. x + cos x

A: Differentiable

Q: Let f(æ) = (42? – 6)°(- 5a² + 9)* 3 12 f' (x) =

A: