2. If p and q are positive integers, f is a function defined for positive numbers and attains only positive values such that f(x f(y)) = x'yª, then prove that q = p².

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

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Q: ´28 – e14z x 0 Determine whether the function f(x) = 14x – 1

A: Solution: Consider the given function is  f(x) = x8-e14x    x<014x-1       x≥0 To check whether…

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: Suppose f(x) = - 2x - cosr. (a) Show that f is strictly decreasing on R. (b) Hence, justify that 2x…

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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: suppose f is a continuously differentiable function satisfying f(3)=6, and f'(3)=5. Find (f^-1)'(6)

A: Given f(3)=6, f'(3)=5  To find f-1'6 By the formula, f-1'x=1f'f-1x And we know that if f(a)=b then…

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

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Q: 16. Suppose that f is differentiable at c and that f'(c) + 0. Show that there exists a ð > 0 such…

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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: Suppose the nonzero function f(x) is infinitely differentiable and that f'(x) = -3f(x) for all a…

A:

Q: Assume that the function f defined by f(x) = 5x+ sin(Tx) is strictly increasing on R and find…

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Q: Find a polvnomial f(x) of degree 4 with real coefficients and the following zeros. 3,-4, 2+i 1) - 0…

A: Given,  The zeroes of the 4 degree Polynomial f(x) is 3, -4 , 2+i and 2-i.

Q: Is there an unbounded function f:[0,1] →R where it is discontinuous only at a single point in [0,1…

A: f: [0, 1] →R Domain: [0, 1] The function is discontinuous at a single point of the domain.   Let's…

Q: Use Theorem 2 to show that 3, if x <-10 2, if – 10 sxso F:R → R,F(x) = -2, if 0< x< 10 -3, if x2 10…

A: so we have to show that given function is discontinuous at 2 and -2 (a)   Discontinuous  at -2…

Q: 18. Suppose that f is a differentiable function such that f(g(x)) = x, and f'(x) = 1 1+(f(x))². Show…

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

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: Consider the function f(x) = In(x + 5) over the interval [1, 9]. Does the extreme value theorem…

A: The given function is f(x)=lnx+5 over the interval 1,9  The extreme value theorem states that if…

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: Prove that f(x) = x 2 takes on the value 0.5 in the interval [0, 1].

A: We have to prove that f(x)=x2 takes on the value 0.5 in the interval [0, 1].

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: 4. Determine if g is differentiable at x = 0 if 2 cos-1 x, if -1<x < 0 g(x) = %3D if x 2 0. x + cos…

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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: Assume that f is a function with domain [0,1] that is differentiable in (0,1). Assuming that f (0) =…

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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: 1. Show that function f(x)=D|x | is not differentiable at 0

A: As per company guidelines we can solve first question. I hope that the given solution will help you.…

Q: Prove that f (x) = x2 takes on the value 0.5 in the interval [0, 1].

A: Here given

Q: Suppose that f is a differentiable function with f(2) = 5 and f'(2) = 7. Let h(x) = f(e*). Find an…

A: Find the derivative for the function h(x). Now, the derivative for the function is the slope for the…

Q: If the function f(x) = {cos(2πx−a),x&lt;−1x3+1,x≥−1 is continuous, what is the value of a?

A: fx=cos2πx-a,  x&lt;-1        x3+1,    x≥-1 Since Cosine function is continuous for all real numbers,…

Q: 4. Show the function f(2)=21m(z) is differentiable or not differentiable at any points.

A:

Q: Prove that f(x) = tan(x) is never negative in 0 < x < ; and show that g(x) = x=l sin x decreases…

A: We have to prove that f(x)=tan(x) is never negative in the interval 0,π2. Then we have to show that…

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: If g(g(x)) is continous at 0, then g(x) is continous at 0.  True or False?

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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: Consider the function f(x) over the interval 0, 1. Does the extreme value theorem guarantee the…

A: Given function is f(x)=1sin πx4 over the interval 0, 1 and  q(x)=4x+32x2-1 Extreme value theorem: If…

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: If the relation x z² - 5xy z-x2-y 0 defines z as a differentiable function of x and y. By using the…

A: Solution

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

A: Given that

Q: The tangent line to y=f(x) at (−8,−5) passes through the point (−3,10). Compute the following f(-8)…

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Q: Suppose f is differentiable with f(0) = 0 and 0 0.

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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: Prove: f(x)=5x y is continuous at x=2

A: A function fx is continuous at a point x=a, if limx→afx=fa Given function is

Q: defines 2 as y. y- cos (3x2) = 5 a function of x and • differentiate implicity to find az ду

A:

Q: 7, The inflection points of the function f(x)%= 글어 -금 + 12-음 ocurs at OCcurs at: ||

A: