III. Verify if the function is continous at the point. 1. f(x) = x³ – 2x² + x – 5 at x = 0

Q: Calculate the approximation for the given functionand interval:                    M4, f (x) =√x,…

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Q: s] B1(a): Find the value of k that makes function continuous at x = 4 x > 4 6x – k x < 4 3x + 6 f(x)…

A: The given function is fx=3x+6if x&gt;46x-kif x≤4. Assume that the above function is continuous at…

Q: B- Find the local extreme points of the function f(x, y) = 4xy - x - y^.

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Q: Suppose ƒ is an even function and Evaluate

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Q: 2 3/2 (1² + 3 + 1)*/² from y = 1 to y

A: Solution

Q: Q1.Given: x? – 4 | when x 3 1.Find what values of ( a) and (b) that will make the function…

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

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

A: Given function is  y=3-t-3,   -1, 5

Q: For æ = 4 the function f(x) = x? + bx +c has the minimum value of -9. Fine

A: The given function is f(x)=x2+bx+c has a minimum value = -9 at x = 4.

Q: find all possible functions with the givenderivative. y' = 1 - 1/x2

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Q: ] B1(a): Find the value of k that makes function continuous at x = 4 | 3x + 6 5х — k f(x) = x > 4 x…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: 5.) Where is the function l(x) = + – 2x + 10 concave up? Concave down? |3D

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Q: 22 If Sx) is an odd function, the second difference [SSAx) – 2(0) +-Ax)]/(Ax)? exactly equals f"(0)…

A: Please check step 2 for the solution.

Q: find the value of the constant ( a, b, or c) that makes the function continuous.

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Q: Locate the discontinuities of the function. 2 f(x) = 1 + e7/x

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Q: Find Fxxygy for the function Fory)-J*J€nx-x]

A: We havr to find the derivative.

Q: 6. The parent function f(x) = Vx is translated 2 units right, compressed horizontally by a factor of…

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Q: Differentiate the function.  u= (1/t -1/square root of t)^2

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Q: Find the value of the constant (a, b, or c) that makes the function continuous.

A: A function fx is continuous at x=a if its left-hand limit, right-hand limit, and fa are equal and…

Q: 3) Let f (x) = e=x² Where is y'> 0? What does this tell you about the original function?

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

A: Given: fx=x2+5x,  -4,0   To Find: The absolute extrema of the function on the closed interval.

Q: find all possible functions with the givenderivative. y' = 5 + 1/x2

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Q: determine if the piecewise-defined function is differentiable at the origin.

A: Consider the given function fx=2x-1,                x≥0x2+2x+7,         x&lt;0 The left hand and…

Q: d) Find the value of the constants ' a’ and b ’ that makes the function continuous at x= 3 ах + b ;…

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Q: Find the absolute extrema of the function on the closed interval.                       y = 3 − ∣t −…

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

A: Solution Given Find the derivative of the functionf'(x)=xx2+1To find the criticle Number derivative…

Q: Find the local extrema of the function f(x)=x2e−x.

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Q: 14. Use the curve sketching procedure to analyze the function. a. y-x'+x²-20x а. 1+x? b. y=- 1-x?

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Q: Which type of discontinuity does the function S4- a², In x, x < 1 f(x) = 1<x < e has at x 1?

A: We need to choose correct option.

Q: On what interval(s) is the function f(x) = x* – 4.x³ both decreasing and - up? concave A

A:

Q: Given the following function: y = x^4 - 8x^3 + 22x^2 - 24x + 2 on [0, 4], find the absolute extrema…

A: To find the absolute extrema of a continuous function on a closed interval [a, b]: Find all…

Q: 4. a) Find the value of x where the function f(x) = (x – 4)5 is not differentiable.

A:

Q: Let f=3x^2+2 and find the values below 1) f(x+h) 2) (f(x+h)-f(x)) 3) lim h→0 (f(x+h)−f(x))/h 4) Find…

A: The given function is f(x)=3x^2+2.

Q: What happens to the function f (x) = 1 + as x approaches to zero.

A: The definition of the function gx=x is given by, gx=x for x≥0=-x for x&lt;0 Thus, the left hand…

Q: 1 For what value of x does the function g(x) =x³ – 2x² concave downward? %3D

A: Consider the function  gx=13x3−2x2

Q: B4: a) Find and classify all critical points of the function f(x) = x³ + 3x? – 12x + 5 b) Determine…

A:

Q: X+1 5) Is the function given by f(x) x2 - 8x + 15 continuous at x = 3? Why or why not?

A: f(x)=x+1x2-8x+15

Q: find the value of the constant (a, b, or c) that makes the function continuous

A:

Q: Determine whether the function is differentiable at x = 2.

A: The given function is fx=x2+1,x≤24x-3, x&gt;2. Sketch the graph of the above function as shown…

Q: Q 5. Find all relative extrema of the following function. f(x)=2x³ – 2x² -2x+1

A: We have to find the all relative extrema of the function: fx=2x3-2x2-2x+1 To find extrema of…

Q: Q1/ Find the local extreme value of the function F(x.y)=4xy – x* – y*

A:

Q: B. Find and classify the extreme points of function f(x, y) = x + y - 4xy-1.

A:

Q: Differentiate the following function with respect to x for y=2e^3x + 8e^9-2x .

A: Given equation is y=2e3x+8e9-2x Differentiate with respect to x.  then,

Q: Find the following characteristics about the linear function 2 f(x) = ²/x + 18 x-intercept:…

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Q: J 3(x)is even function

A: Bessel Function The property of Bessel function says that- (1) Jnx is an even function when n is…

Q: Clear my choice The absolute minimum value of the function f(x) = 7x² – 14 + 6 over the interval [0,…

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Q: 14) What is the domain of the function f(x) E, ?

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Q: 9. If f(5) = 13, f' is continuous, and f'(x) dx = 16, what is the value of f(6)?

A: Use property of definite integration

Q: 3. Given the function g(x) = x - 2x2 + x, find the interval(s) when g is concave up and decreasing…

A: We have given a function g(x).  We have to find the interval where g is concave up and decreasing at…

Q: 6. What is a point of inflexion ? Does f(x) = x' have a point of inflexion at x = 0?

A: Given that,

Q: 19. Find the absolute extrema of the function on the indicated interval. f (x) = xe-3x;[-1,2] хе

A: As a first step, we need to find all the critical points by equating the derivative of f(x) to zero.…