a = 0; [0, 2) (3-x² if x > 0 – x2 f(x) = { (-2x + 3 if x < 0 The function is differentiable at the given value of a. The function is continuous at the given value of a. The function is differentiable at the given interval. The function is continuous at the given interval.

Q: Consider the function f(x)=xe−9x,0≤x≤2. On this interval, ff has a minimum value equal to: which is…

A: Given fx=xe-9x 0≤x≤2

Q: 2) Consider the function g(x) = x3 + 3x2 – 9x + 2 on the interval [-4,2]. Find all local extrema,…

A: According to our company policy we can only answer the first question and rest of the questions can…

Q: If f is a differentiable function and such that and g(x) = x+2 / 1+f(x) such that f(0) = -2 and…

A: Given: gx=x+21+fx f0=-2 and f'0=5 We have to find the value of g'0.

Q: Xs-1 Let f(x) = {[x+1]-[1-x). -1<x<1 x21 1x|x- where [] denotes the greatest integer function, then…

A: Introduction :

Q: Let g(x) = x4 – 2x² + 1. (a) Find all critical points of g. (b) Find the absolute maximum and…

A: Given: a)      gx=x4-2x2+1  Critical points:        Critical points are the points where the…

Q: 2. Find the absolute maximum and minimum values of the function f (x) = - on the closed interval -2…

A: We need to find absolute max and min value in given interval.

Q: 3. GIVEN: ƒ(x): 2x2 – 3 xs2 (8x-11, x>2 DISCUSS THE DIFFERENTIABILITY OF THE GIVEN FUNCTION AT x = 2…

A: Given query is to determine whether f(x) is differentiable at x=2 or not.

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Q: 6. Determine all values of x at which the function is discontinuous. x2- 2x +5 f(x) = x2-4x 0, 4 O…

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Q: ) Find the values of the constant a so that the function f (x) will be continuous for all x. fax +…

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Q: Find the absolute maximum and minimum of the function f (x) = x³ - x+2 on the interval [0, 3] %D

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Q: Find the location of the global maximum and minimum of f(x) = x^3-6x^2+1f(x)=x3−6x2+1 on the…

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Q: If f(x) is a differentiable function such that f'(-2)=-1 and g(x)=f(3x+1), then what is g'(-1)?

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Q: 4. Given xo < x, and x, define x - xo X1 - X0 and let P1(x) interpolate the function f(x) at the…

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Q: A Function f(x) is defined for all xr>0, and satisfies f(x2) = x3 for all x > 0.Show that f is…

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Q: Find the value of k so that the function 5x+3 if x<3 f(x) =. kx2 if x 23 is continuous everywhere?

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Q: Over the interval (0,2), the function f(x) = (-x²) e*

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

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Q: A cubic polynomial function f is defined by f(x) = 4x3 + ax2 + bx + k where a, b, and k are…

A: f(x) = 4x3+ax2+bx+k local minimum at x=-1point of inflection at x=-2At point of inflection ;…

Q: 1 The function h(x) can be expressed in the form f(g(x)), where g(x) = (x + 3), and f(x) is x + 3…

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Q: -3x² + 5x – 12, x 2

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Q: 1. Find all critical points for the functions: a) f(x) = x² – 10x – 9 5 – x b) f(x) = x² – 6x + 30 -

A: As per our company guidelines we are supposed to answer only first question. Kindly repost other…

Q: 7. Find the absolute maximum and minimum, if either exists, for the function below on the given…

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Q: For what value of the constant c is the function f continuous on (-o S cx2 + 8x x3 – cx if x 3 с 3

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Q: The equation for a family of functions with zeros at +3, and -1, with end behaviors from Q2→Q4 is:…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: If the function f (x) = {_ 4x + 8, x3 is continuous at x = 3, then the value of k is O a. -2 O b. -6…

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Q: The function f(x) has a continuous second derivative, and it satisfies f(8) = -4, f'(8) = 0 and…

A: The function f(x) has a continuous second derivative, and it satisfies f(8)=-4,f'(8)=0 and f''(8)=1.…

Q: Please show step-by-step solution

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Q: if x 2 1. Determine the constant k such that the function f(x) = is continuous at x = 2.

A: As per guidelines, I can answer maximum one question. Since you have asked for multiple questions,…

Q: Find the absolute maximum and absolute minimum values of f on the given interval. ln(x^2+3x+8) in…

A: Given:

Q: 1) Find the absolute extremum values of f(x) = x2 – 2x + 9 over the interval [1, 2).

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Q: The function f(x) = x'-3x has a local maximum at x = %3D O A. OC. С. -2 D. 1 B. 2.

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Q: nd all the critical points of the function f(x)= ={ x² 23 if x<1 if x ≥ 1

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Q: The function h(x)=1x+7h(x)=1x+7 can be expressed in the form f(g(x))f(g(x)) where…

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Q: Find numbers a and b such that the given function g is differentiable at 1 g(x) = ax*3-3x, if x1

A: Consider the given function  gx=ax3-3x   if x≤1gx=bx2+2     if    x&gt;1

Q: -3x2 — 16х — 16 x + (-4) f(x) = 4x2 + 23x + 28 С, X = (-4) What value of C would make f(x)…

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Q: Find the absolute maximum and minimum values of f in the given interval. f(x) = x* – 2x² + 1, (-2,…

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Q: 5 The function g(x)= hx²-4x + k has a minimum value of -1 when x= 1. Find the value of h and %3D %3D…

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Q: 22 + За — 70 x + -10 f(x) = x² + 8x – 20 C, x = -10 What value of C would make f(x) continuous at x…

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Q: 4. If f(x) is any polynomial of degree 10, then the 9th derivative of f (x) is zero. 5. If f'(0) =…

A: A detailed solution is given below

Q: Find the absolute maximum and minimum values of f on the given interval\ f(x)=e^x/(1+x^2)     [0,3]

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Q: The function f(x)=(a-x)2/3 has domain R and only one critical point x= a. Use a number line to find…

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Q: 2. The equation for a family of functions with zeros at +3, and -1, with end behaviors from Q2→Q4…

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Q: Find the critical points of the given function. a) f(x) = √2²-4 b) f(x) = 3x + 21-1

A: To find the critical points of the given functions.

Q: 6) Find the value of c such that {0, c} is 2-cycle such that c be a constant and let the function be…

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Q: Given: F(x) = 2x2+ 1, G(x) = 2x - 1, H(x) = x H-1(x) = -x x 1/x

A: For finding the inverse of H(x)

Q: *show work*

A: Given:A continuous function y = f (x) is known to be negative at x = 4 and positive at x = 9.

Q: If f(0) = 0 and f"(x) exists for all x>0, then show that f'(x) – f(x) 1 xf"(5), 0 < § < x. %3D Also…

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Q: 3. Find the value of the constant k that makes the function continuous f(x) = {x² – 6, x + 4k, x 6

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Q: Find extreme values of the function over its natural domain. (a) f(x) = x³ + x² – 8x + 5 (b) f(x) =x…

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.