|(2) = { = 1 points are the functions continuous? 3x-5 , ifx 1 .ifx 1 1. 2 2. h(x)

Q: If ƒ(x) = x^n, n>=1, show from the definition of the derivative that ƒ′(0) = 0.

A: Given,

Q: im (x²-C² if X<4 1 f(x) = {(x+5 x²-c² (x + 5 if x = 4 lim

A: Given:-x2-c2   if x&lt;4cx+5    if  x≥4f(x) is continuous at x=4solution:-if f(x) is continuous at…

Q: 4. Is the function given by G(x) 1 x-1 the interval (0, ∞)? Why or why not? continuous over

A:

Q: 2) Use the limit definition to find the derivative of the given function. y = 3r2 – 2x

A: Limit definition of derivative is f'(x)=limh→0f(x+h)-f(x)h

Q: 1 Is the function given by f(x)= 3x+2, for x ≤ 3, 4x-7, for x>3, continuous at x = 3? Why or why…

A:

Q: Find the derivative by the limit process. f(x) = 11 – x2

A: We have to find the derivative by the limit process where f(x) = 11 – x2.

Q: Use the first derivatives test to find local exterma of f( x) =x3 -12x on R

A:

Q: Vx + 2 Determine where f(x) = is continuous. In(3x – 5)

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Q: For what value of the constant c is the function f continuous on (-∞, 00)? cx2 + 2x if x 2.

A:

Q: The function y = 1/x does not take on either a maximum or a minimum on the interval 0 &lt; x &lt; 1…

A: Extreme Value Theorem:If a function f(x) is continuous on a closed interval [a,b], then f(x) has…

Q: 2. Is the function given by f(x) = 3x - 2 continuous at x = 5? Why or why not?

A: Is the function given by f(x) = 3x - 2 continuous at x = 5?

Q: If f(x) = etan-¹(x²-3) then f'(x) at x = 2 is equal to

A: SOLUTION-

Q: Find two paths of approach from which one can conclude that the function has no limit as (x, y)…

A: Let X2=mY , where 'm' belongs to set of integers. And here we have taken a parabolic path .

Q: If - 2x +1 ,when X#! and fcx)= 3 when x= 1 show that The function fex) Continuous at X - 1

A: The detailed solution is as follows below:

Q: Find constants a and b such that the function 3– bx, if x>-2 f(x)=- -1, if x=-2 ax – bx, if x<-2 |…

A: Given query is to find the value of a and b.

Q: At what points is the function is continuous y=|2x-1| +4sin(2x)

A:

Q: I. Is the function given by g(x)=x²-3x + 2 continuous over the interval (-4, 4)? Why or why not?

A: Function given is- g(x)=x2-3x+2 continuous over the interval (-4,4) . Wee need to determine whether…

Q: True or FalseA 1. A Step-function is continuous at every point in its domain

A: Given: A step - function is continuous at every point in its domain. To write: The given statement…

Q: For what value of the constant c is the function f continuous on (-∞, 0)? cx2 + 8x x3 - cx if x < 5…

A:

Q: 49. Is the function given by g(x) = x² 3x continuous at x = 4? Why or why not?

A: Given: g(x)=x2-3x Determine the limit at x=4. limx→4g(x)=limx→4(x2-3x)

Q: Find all possible functions f with the given derivative. f'(x)= 1/x-1, x is greater than 1

A: Obtain the all possible functions as follows.

Q: For what value of the constant c is the function f continuous on (-∞, 0)? { cx2 + 5x if x 4

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Q: 10 if x c - everywhere then: С —

A:

Q: If the function is defined y=2x when x=3, is this function differentiable at x=3? Also, is this…

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Q: X = (1-_-_-_-)* 2 o then f(x) tend:

A:

Q: State why the function 2z2 - 3z + e-z is analytic everywhere.

A: See the answer below

Q: 1. If F(x) = - eta dt, find F(1) and F'(x).

A: If Fx=∫exe et2 dt, then to find F1 and F'x.

Q: x² – 16 f (x) = x( x 2(х — 1)°(х — 2) : о 1)8 (x – 2) : 0 - -

A: If the given function is equal at LHL and RHL at x=3 then the given function is continuous at x

Q: Let f(x) = Cx + 7x if x< 4 x³ - cx if x2 4. For what value of the constant c is the function f…

A:

Q: Find the absolute extreme of the function on the closed interval y = 3cosx ; [0,2π]

A: To find the absolute extreme of the given function.

Q: [4] 2. Find f'(x) using the limit definition of the derivative. Credit will not be given for any…

A:

Q: Find y' if y = 5x + 2 using the limit definition of derivative.

A: Given that  y=5x+2

Q: Shows that if a function f(x) is continuous in interval [a,b] then most likely the derivative of…

A:

Q: At what points are the functions continuous x+3 y =- 3x, Зх, y = y = (2x – 1)3 х-2 x2 -3x-10'

A: To find the points where following functions are continuous y=1x-2-3xy=x+3x2-3x-10y=2x-113

Q: What are the maximum and minimum values of the function y = | x | on the interval -1 ≤ x &lt; 1?…

A: Use the graphical approach to determine the maximum and minimum values of the function y = | x | on…

Q: Use the second derivative test to find the local exterma of the function f(x) =x3+12x2-5 on R

A:

Q: For what value of the constant c is the function f continuous on (-∞, 0)? if x 5 C = Need Help?…

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Q: Find the value k that makes the function continuous. kx f (x) = x > 9 - -7x – 7, x < 9

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Q: f (x) %3D х3 -Зх2- 2 3x2

A:

Q: What is the limit that will calculate the derivative f'(2) for the function f(x)= x-1

A: solution of the given problem is below...

Q: consider a continuous function y=f(x) whose first derivative is y'=x(x- 2).

A: We can find the interval as below.

Q: For what value of the constant c is the function f continuous on (-∞, 00) ? if x < 3 cx2 + 8x F(x) =…

A: To find: The value of c if function is continuous at -∞,∞. Given: The function is fx=cx2+8x   if…

Q: 5. Use the Second Derivative Test to find all local extrema of the function below. (3 points total)…

A: To find the local extrema of the given function f(x)=x4-4x3+2

Q: 2. Is the function given by F(x) = x². 5x + 6 continuous over the interval (-5, 5)? Why or why not?

A:

Q: 4. By the definition of derivative prove that f(x) = √x² +5 is differen- tiable at x=2.

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Q: 1. Use the first derivative test to find the location of all local extrema for 3 f(x) = -x³ +x+ 18x…

A: Dear student as per our rule in one session we can only solve one question. Please post the other…

Q: x+4 if x2

A: