1. Let f(x)= x on the interval [-7r, 7T. (a) Compute f42, given by 1/2 -T

Q: Find a first degree approximation of f (x) = In x centered at x = 1.

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 5. Show that the function h(x, y) defined by if r2 + y? 1 is discontinuous.

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Q: The graph of f(x)= - x2-1 is concave up on interval (-1,1)^O (0,1) 0 (-1,0) U (1, 0 ).co (-∞, – 1)U…

A: Given, fx = xx2-1  We have to find the interval in which graph of  fx = xx2-1 is concave up.

Q: Find the absolute maximum and absolute minimum values of f on the given interval. 8. f(x) = 2³3r² -…

A: In this question we have to find the absolute maximum and absolute minimum.

Q: If f(x) = In(tanh(2æ)), then f'(x) is %3D Select one: O a. coth(2a)sech (2r) O b. 2 coth(2a)sech…

A: Given: f(x) = ln(tanh(2x))…

Q: a2f b- For the following functions prove that ax2 ay2 1- f(x,y) = e-2y cos 2x %3D f(x,y) = In/x2 +…

A: The first step inludes the  partial differentiation of the functions individually with respect to y…

Q: 1 Find the interval on which the curve F(x): -Sa di is concave downward. 6+ 8t

A: Solve the following

Q: on f(x, y) = 3x + 9y subject to th %3D

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Q: 4. Integrate the function f(z) = z² + 2z from z = -i to z = 1 in two ways, once along a straight…

A: The objective is to integrate the function fz=z¯2+2z from z=-i to z=1 in two ways, Once along the…

Q: 2. Let f(x) = S dt for x 2 2 In a) Find F'(x). b) Is F increasing or decreasing? What can you say…

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Q: 1. Consider finding the root of f(x) =x´ – 5 use secant method, ɛ = 0, and start with the a interval…

A: given , f(x) =x2 - 5  we have to find roots of f(x) in interval by using secant method

Q: 1. Given the function 2r + 1, r 1 Verify whether or not the function f is continuous at r 1.

A: the given function is: fx=2x+1,     x≤14x2-1,       x>1 we have to verify whether or not the…

Q: I'm stuck on this question and I don't know how I should be approaching this. What should I do?

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Q: 1 Let f(x) = 8 + In (t) dt, for x2 1. Find f'(2).

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Q: 4) Determine the function F(x)=[ƒ(1)dt, where ƒ(x)=sgn(x-x²) for xe[-1,2]. -1

A: f(x) is discontinuous but F(x) is continuous

Q: Consider the function f(x) = ex – 1, the third approximation of the zero p, of f using Nweton's…

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Q: 1 - t Let F(x) = dt for -o << x < +∞ t2 + 24

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Q: Suppose that f and g are discontinuous at x = c. Does it follow that f + g is discontinuous at x =…

A: Let us define that Then both f and g are discontinuous at x=2

Q: 45. For what value of a is x2 - 1, x < 3 2ax, f(x) = %3D 2ах, continuous at every x?

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Q: -Q3/As the function f(x,y) = at (-1,2) xy 1 + x² + y² is Continuous

A: Here we have to check the continuity of the function at the given point.

Q: 4. Find the first two intervals using the bisection method to compute the minimum of the function…

A: We need to find the first two intervals of on the interval

Q: 9. Show the function f(z) = 1 + 2i+2Re(z) is differentiable or not differentiable at any points.

A: Solution

Q: 19.D. Show that the function defined by g(x) g² sin (1/x), x * 0, %3D = 0, 0, is differentiable for…

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Q: Please just do 1(b)

A: To compute the required value , by definite integral

Q: 2. Determine if a function f : [0, 27] → R defined by f(x) = sin 2n is continuous.

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Q: attached

A: Linearization of f(x) at x=a is given by

Q: make a sketch of the given function on the interval[0,∞).

A: Given: To Plot:

Q: Find the absolute extrema of the function on the closed interval.

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Q: 11. Prove from the definition that the following functions are differentiable. ()- (b) f =xy?

A: By the definition, the function f(x,y)=xy^2 is differentiable if fx(x,y) and fy(x,y) both exist.

Q: 2.4 Use the definition of the derivative of complex function to show that f(z) is not dif-…

A: The Complex Derivative Definition: Let f be a function defined on a neighborhood of z0 ∈ ℂ. If…

Q: C. Is the function define by g(x) = x² – sin x + 5 continuous at x = n?

A:

Q: Consider the following equation defining the function f on the integers implicitly: f(n) = n+ f(n –…

A: Given:            f(n) = n +f(n-1),  f(1) = 1

Q: Find the best linear approximation to f on  the interval [-1,1].                        f(x) = x2

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Q: The graph of f(x)= x2 -1 is concave up on interval (-1,1)^O (0,1) 0 (-1,0) U (1, 0 )co…

A: Given,  The function fx = xx2-1  We have to find the interval in which the graph of  fx = xx2-1 is…

Q: 2. Consider the function f with domain (-2, 0): 3|22 – 1| if – 2<r<1 2.r2 + 2x – 4 f(x) = 3 if r = 1…

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Q: d. Find the linear approximation L(x) for f(x)=x²-x-1 at a = 1.

A: Given function is fx=x3−x−1. d We have to find the linear approximation Lx for function fx at a=1.…

Q: 18. Consider the function f (x) 5e2r. On what interval(s) is f (x) %3D increasing? On what…

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Q: 3. Given that f(r) = dt. Determine the interval(s) on which f is increasing. %3D 3+t

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Q: Suppose h(x) = [,f(t)dt on the interval [0, 12], where f (t) is shown in the graph below. f (t) -4-…

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Q: Find all the x-intercepts of f(x)=cos(x) on the interval [0,2π)

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Q: The function f (x) ,x € [-27, 2n] is continuous on: 1-cos x

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Q: Q.4 A/ Prove the function continuous at x = -2, (x2 + 5 13-3x where %3D if x<-2 if x 2-2 f(x) = %3D

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Q: 2. Find the (exact) values of a and b so that f is continuous at a = 2. 8r2 + 20x + 28 if x 2

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Q: 34. Show that f(x) = Jã is not differentiable at x = 0.

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Q: 2. Determine whether the following functions are linearly dependent or not by applying the…

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Q: 2. Consider the function f(x) = if x = {9 in lowest terms q > 0, p,q e Q; 0 if x e Q°,x = 0…

A: We use sequential approach of continuity to show it.

Q: Let f : (0,∞) → (0,∞) be given by f(x) = ln(2 + x). Prove that f has a fixed point located between 1…

A: The given problem is to prove that the function f(x) has a fixed point in between 1 and 1.2 Given…