| 2) Prove or disprove that the following functions are 1-1 a) f(x) = x5 +1 b) f(x) = x1 -6 3) Given f(x) = x3 +7, find (f-1(6))' 4) Given f(x) = x + Vx, find (f-1 (2))' 5)/Given f(x) = x5 + 3x - 2, find y (f-1(x))' at the point (2,1). 6) Given f(x) = x3 - 3x- 2, determine restricted intervals where fwoul function.

Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: Given: fx=2x−1x2+3x2+1, and gx=x2+872−3x25 To check whether: f'x=4x2x2−1+2xx2+3−2xx2+12x2−1x2+3x2+1,…

Q: The tangent line to y=f(x)y=f(x) at (−3,−2)(−3,−2) passes through the point (−4,−3)(−4,−3). Compute…

A:

Q: 1. Verify that the Mean Value Theorem applies to the function f(x) = v25 – x² on the interval [-3,…

A: Use mean value theorem

Q: 2. If f(x) = cos2x, find f(0), f(--).f),f(-x) 3. If f(x) = x(x+1), show that f(x+h)– f(x)= h(2x +1+…

A: 2. f(x) = cos2x , find f(0) , f(-π/4), f(7π/8) ,                                         f(-x). f(0)…

Q: 11. Use the Mean Value theorem to show that f(x) = 2x sinh (æ – 1) + 2" – x has a critical number…

A:

Q: Let f(x) =x sin x and g(x) =x cos x. (a) Show that f'(x) = g(x) + sinx and g'(x) = -f(x) + cos x.…

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Q: ,x 1 Is the function k(x) = {x²-1 2,x = 1 continuous at x = 1?

A: We use L' hospital rule to find the limit.

Q: 6 Use the Linear Approximation to estimate Af for f(x) = when a = 2 and Ax = 3+x2 (Use decimal…

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Q: Use the Intermediate Value Theorem to show that there is a root of the given equation in the…

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Q: Consider a function f with domain (xx 0} and the following derivatives: f(x) = bx-1 and f (x) = bx…

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Q: Suppose ff is differentiable on (-\infty,\infty)(−∞,∞), f(3)=12f(3)=12, and f'(3)=-2f′(3)=−2. Use…

A: Given that,  Function f is differentiable on (−∞,∞), f(3)=12, and f'(3)=-2. The linearization of f…

Q: 1. Let f(x)=x+sinx in the interval [0,2x] a. Determine algebraically all critical values of f(x).…

A: Maxima or minima: f(x) is any function 1) put fx(x)=0, for critical point. 2) Find fxx(x) at…

Q: 5. Prove f(x) = e* + x has a root on the interval (-1,0) using the Intermediate Value Theorem.

A:

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. Show that a frination fiłamb ]->1R is differentiable at xolamb) is and only if its lower and…

A: Solution: f:[a,b]→ℝ is differentiable at x0(a,b). Let us take upper derivative at x0+. Then,…

Q: (b) Let f(x) = 12x35+ 15x* – 40x³ + 17. Find the critical numbers, and show what the Second…

A: f(x) = (12x 5+15x4 -40x3 +17.   critical points   f'(x) = 0   60 x4 + 60x³-120x²  = 0.   x² ( 60…

Q: 2. Use the Mean Value Theorem to show that f(x) = 2x sinh(x - 1) + 2* – x has a critical number…

A:

Q: 2. Use the Mean Value Theorem to show that f(x) = 2x sinh(x – 1) + 2" – x has a critical number…

A:

Q: Use the Intermediate Value Theorem to show that there is a root of the given equation in the…

A:

Q: for x 2 - X Is differentiable at x = 2 but not at x = 1.

A:

Q: 4. Find the maximum value of f (x) = In(x – In x) on the interval -sse. e

A:

Q: 5. Show that the function f (x) has roots between (0,2) x² + 2x – 3 f(x) x - 1

A: To show the f(x) has roots between a and b we have to show that

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

A:

Q: 1. Employ the following methods to find the maximum of f(x) = 4x – 1.8x² + 1.2x – 0.3x* (a)…

A: Given f(x)=4x-1.8x2+1.2x3-0.3x4. To find: (a) find the maximum using golden search method.…

Q: , 6]. che function on this interval. 1/sqrtx ow there exists a c in the open interval (2, 6) such tl

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Q: 16. Show that f(x) = Vx - 2 is continuous at x=2 but not differentiable at x=2.

A:

Q: Show that f(x) = x – cos(x) has only 1 real zero on the interval [0, .

A: given fx=x-cosxx∈0,π2

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<-11-x2 if -1≤x≤1x2-1  if x>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: 20. The function f is continuous at x = 1. Vx + 3 -. - V3x + 1 for x 1 x - 1 If f(x) = k for x = 1…

A:

Q: 1. Let f(x) = 4x − 4x 2 . Verify that f(x) satisfies the conditions of Rolle’s Theorem on the…

A: Note:- According to the company policy we can attempt ?️ only one question so please upload the next…

Q: 1. Consider the following function: f (x) = x² + 8x cos y 2x + 10 cos y – 8 cos² y + 8 cos y, x =…

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Q: Find the value of K that make the function f continuous at x=2 -4 スー3x+2 sin(nx) + kx + k if x 2

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Q: Let f(x) be a function with second derivative of f"(x) = -(5x +11)?(x – 2) Determine the local…

A: When a function's at critical point x , and the second derivative at x is: less than 0, it is a…

Q: Let g(x) = x - 3x. (a) Determine the critical points of g(x). (b) Use the Second Derivative Test to…

A:

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

A: Given the function f(x)=x2−2x+1 On the interval [−1,3]

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: The Second Derivative Test cannot be used to conclude that x = 2 is the location of a relative…

A: We need to check for which of the given functions, can't conclude about location of  a relative…

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) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: We use the quotient rule, product rule, and chain rule of differentiation to check the claim of the…

Q: 3 - x, x<2 Q.No.15: Is f(x) = {+2 x22 continuous at every x € R. x+1 xs1 -.

A: Continuity of a function.

Q: 5. Show that the function f (x) has roots between (0,2) x² + 2x – 3 f (x) = X - 1

A: Given that

Q: 2. Consider the function а(т — 2) Vx +2 – 2 - if x 2, 2x 2 x² - where a, b, c are real numbers.…

A: Given function is  f(x)=a(x-2)x+2-2   if x&lt;2b                     if x=21x-2-cx2-2x  if x&gt;2…

Q: 7. Verify the validity of the Mean Value theorem of Lagrange in the case of f(x) = 2x3 – x +1 in the…

A:

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: If f(x)=sin-'x. Show that (1-x2) fx(x)-xf (x)=0. HENCE ,prove that f^(n+2)(0)=n²f^n(0)

A: