11. The function f: R – {-2} → R is defined by f(x) : x+2 Determine f'(1) and verify your answer with an ɛ – &8 proof.

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

A:

Q: The following statement is false, explain why. The function g(x) = x^2 on the interval [-1,1] has…

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Q: 34) If f is an even function that is continuous on [-1,3] and if f f(t)dt f₁f(t)dt = 8, then f…

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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: 3. Show that the functionf on [-1,1] defined as if f (r) = 1+e if x = 0 is discontinuous at x = = 0.…

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Q: 3. Compute the value of F.dr if F = -yi + xj and C is a semicircle from (-1,1) to (1,-1).

A:

Q: (5) Use the limit definition of derivative to prove the following: (a) For any a e R, (f(ax))' =…

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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: Q1: If the function f(x) define as f: R→ R such that f(x) = (x+1, x>2 x²-1, x≤2 Show that the…

A: This is the question to check the differentiability of the function.

Q: Find the linearization L(x) of f(x)=tan x at x=3pie/4.

A: Given

Q: Suppose F 1  and F 2 are both antiderivatives of f on an interval I How are  F 1  and F 2  related?

A: Given:  F 1  and F 2 are both antiderivatives of f on an interval I. That is,

Q: (b) Show that the u(x, t) can be written as u(x, t) = 0(x – at) + 4(x + at), where o and are…

A: The multivariable function u(x,t) is a rule that associates or fixes a number to a particular point…

Q: Prove that f(x) = [[sin²(2log r)– 3 sin ( 2logt)+2] dt %D 1. Cannot be decreasing any where,

A: To prove that f(x) can not be decreasing anywhere, where f(x) is defined as…

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: 4 Given that f(2) is analytic at z = 0 and that f G) =, n = 1,2, 3..,find f(2). VE

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Q: 4. Verify Rolle's Theorem for f(x) = x² – 2x +1 on [-1,3]

A:

Q: 4. Verify Rolle's Theorem for f(x) = x² – 2x + 1 on [-1,3]

A: Verify Rolle's theorem

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

A:

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: Show that the function f : [0, 1] →[0, 1] given by f(x) = (x −1)2 has a fixed point. Can you apply…

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Q: f(z) = z2

A: We have to show the given function is not analytic at any 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: b- For the following functions prove that ax2 ay2 1- f(x,y) = e-2y cos 2x %3D 2- f(x,y) = Inx2 + y2…

A:

Q: The graph of f(x)= x2 - 1 is concave down on interval | (-1,1) ^O (0,1) BO (-1,0) U (1, ∞ )co (- 00…

A: From the given problem:   fx=xx2-1   As we know that for concave downward:   f''x&lt;0   So,…

Q: 3. Consider the function Prove that f'(0) = 0. & f(x) = if r EQ if x & Q.

A: Introduction: A differentiable characteristic of 1 actual variable is one whose spinoff takes place…

Q: (11) (C) For the function f(x) = x° – x, determine whether the hypothesis of Rolle's theorem hold on…

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Q: X if x e Q If f (x) is defined on [0,1] by the rule f (x) = < (1-x , if x 4 Q Prove that fof (x) = x…

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

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Q: 9. Consider the function f: R → R, defined by (x²sin(1/x) ifx # 0 f(x) = if x = 0 Then a. f is not…

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Q: 4. In f(x) = {1– x² if -1sxs 1. Is the function continuous at x=1? Prove. (x² – 1 if x > 1

A: Given Function:                  f(x)={x2-1, if x&lt;-11-x2 if -1≤x≤1x2-1  if x&gt;1    To…

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

A: We can solve this using R.H.L ≠ R.H.L

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: Let f be the function defined on [0, 1] by when x is irrational, f (x) = 1 when x is rational.…

A: Please see the below picture for detailed solution.

Q: Suppose that f(x) is continuous on [0, 9] and Fx) is an anti-derivative of f. If (0)=9 and F(9)=3,…

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Q: For the function f(x)=sin(x)/x defined on [-1,1], there is some -1<c<1 such that f′(c)=0.f′(c)=0.…

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Q: 1. Use the definition of the derivative of complex function to show that f(z) is not differentiable…

A: We will show the given statement.

Q: 1. Consider the function z = f(x, y). If fa(a, b) and fy(a, b) both exist, and they are equal, then…

A: 1. Given: z=fx,y and suppose that fxa,b and fya,b both exists and they are equal and it is…

Q: The tangent line to y=f(x) at (7,0) passes through the point (6,−7). Compute the following. a.)…

A: Topic:- calculus

Q: A function f is defined by f (x1) = / Cos(x – t) os(x-t) dt cos(t) f (x) : 01 Simplify f(x) and…

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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: 2. The function (x) = x² is differentiable at x = 1. Find the function & such that o(x) = o(1) +…

A: Introduction: A technique for determining a function's derivative is differentiation. Mathematicians…

Q: Suppose f is a function such that f(z) = 4z' and f" (z) = 12z. Which of the following is TRUE? f has…

A: Suppose f is a function such that f'(x)=4x3  &amp;  f"(x)=12x2

Q: Show that there exists an x in the interval (0, 1) that satisfies the given equation V = 1-x Hint:…

A:

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…