6. Let g(x) Find the domain of g(x). x-4' 2x2-3x+7 7. Let f(x) = Find f(3),

Q: 4. Is the function f(x) = (x + 1 ((x-4)² +3 ; x<4 continuous at x = 4? Why or why not? ; X24

A: Since you have asked multiple question, as per company guidelines we will solve the first question…

Q: 2. Let f (x) = x² + 3x – 5. а. Use the formal limit definition of the derivative to compute f'(x).

A: Given,          fx=x2+3x-5

Q: x²-1 If f(x) = for x +1 and f(x)=2 when x 1, show that the function x-1 is continous at x=1?

A: Show that f is continuous at x=1

Q: G. Find the derivative of the following functions using the limit definition. 1. g(t) = 2-5t 5t+2 2.…

A:

Q: 4. Consider the function f(x) = Vx – I (a) Use the limit definition of derivative to find f'(x)

A:

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

A:

Q: 5. Show that the function f(x)= 3x-9 is not differentiable at x=3. Find the formula for f'(x).

A: To Prove: Show that, given function is not differentiable at x = 3.…

Q: Let f(x)=x+(1-x)^(1/2). Find the local maximum and minimum values of f using both the first and…

A:

Q: c) lim,→1+ f(x) where f(x) = { V1- x, x 1 | x +1,

A: Given query is to find indicated limits.

Q: Determine the limit of f(x) as x approaches 2. * 51 f(x) 4- 5 4 2 -i 0 i 2 3 4 5 1- -2 3 5+ 3 1 DNE…

A:

Q: 7. Is the function given by G(x) at x = 2? Why or why not? 1 x² - 6x + 8 continuous

A: Theory : If A function f(x) is continuous at some point a, then it must satisfy All of these…

Q: 4. Given f (x )=x'-12x +1. Use the second derivative test to determine the local extremum off (x).

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

Q: 5. Use the second derivative test to determine whether f(x) has local maximum or local minimum at…

A: The function is given by f(x) =-2x3+6x2-3 To evaluate : The point of local maxima or local minima.

Q: Find the local maximum and minimum values of f using both the First and Second Derivative Tests. (If…

A: Differentiate the function fx=xx2+1 with respect to x, to obtain f'(x) and f''(x).…

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: Compute the derivative of f (x) = x 1/3 using the limit definition.                            (x +…

A: Given: fx=x13 To Find: The derivative of the given function using limit definition

Q: 2. If function f(x) = 3²-12 is continuous at x=2, find f(x). x-2

A: We need to find f(x).

Q: 4. Consider the function f(x) = Vx – 1 (a) Use the limit definition of derivative to find f'(x)

A: Ans:- Consider the function f(x)=x-1(a) we have to use the limit definition of derivative to find…

Q: when x # 1 Show that f(x)% = 2 when x =1 is discontinuous at x 1

A: Given query is to find the continuity of the function at x = 1.

Q: 1. Use the limit definition of the derivative to find g'(x) if g(x) = 2x² – 6x + 13.

A:

Q: 3) Let f(x) = 3x – 1. Use the limit definition of the derivative to find f'(x).

A:

Q: f(z) = z2

A: We have to show the given function is not analytic at any point.

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

A:

Q: 66. What will be the function g(x) resulting from normalizing the function f(x) = x³ − x4 defined in…

A: To find : function gx resulting from normalizing the function fx=x3-x4 defined in the domain 0, 34

Q: Find the value of k that makes function continuous at z = 4 | 2x + 8 x> 4 4x k x < 4 f(x) =

A: If the function is continuous at x=4 then the left and right-hand limit at x=4 should match. That…

Q: 3- Show that this function is differentiable for all and find its derivative (2) = f(x+ jy) = x*-…

A: The necessary and sufficient condition for a complex function f(z)=U+iV  (where U,V are the real and…

Q: 2. Use the limit definition of derivatives to find the expression for f'(a) for the function 1 f(x)…

A: Here ,               We have given a function now we have to solve it by using definition of limit…

Q: 2, if x 1

A: The given function,  f(x)=1x,if x≤1x2-1,if x&gt;1

Q: In the fucntion:  f(x)= (12-3x)(e^x)  When is the function concave up and concave down in interval…

A: Given,f(x)= (12-3x)(e^x) By definition,

Q: 3- Show that this function is differentiable for all and find its derivative f(2) = f(x+jy) x - 15x…

A:

Q: Find for the following function: 1- y = etan'x 2-x'y+ x*y 2 at x = 2

A:

Q: - Find f (x) given f' (x) 6x2 - 4x + 3 and (2, 15) is on the curve of f (x) .

A: To find the function from derivative we need to integrate.Here we will integrate to find f

Q: If f(x) = etan-¹(x²) then f'(x) at x = 1 is equal to TU 2e4

A: The explanation of answer as follows :

Q: Given f(x)= x² and  g(x)= 4x+1 if x>2          = x²+5 if x≤2 a)use the limit definition of…

A:

Q: 9. f (x) = (1– 2x)* find f'(x) %3D 10. Iff(x) = \x find f'(4). 11 Use the limit definition to find…

A:

Q: (B) Let f(x) = 3x – 1. Use the limit definition of the derivative to find f'(x). %3D

A: Explanation of the answer is as follows

Q: #4) Given the function f (x) =x³-x² +2x- 1. Use the second derivative test, where applicable, to…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: If 7x-5,x < 1 h(x) 3x2 – x, 1 < x < 3 Is h(x) continuous at (x=1)?

A: Given: hx=7x-5,x&lt;13x2-x,1&lt;x≤3 We know that any given functiony=fx will be continuous at x=a…

Q: 8. For the function: 2 f(x) x +3' use the limit definition of the derivative to find f'(x).

A:

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

A:

Q: 4. Find the point on the graph of f(x) 5x + 20x – 3 where the tan gent line is horizontal. 5

A:

Q: Find the extrema of the function g(x) = x3 using any of the methods given in the above discussion.

A:

Q: 2.Given f(x)=5Vx-1, find f'(x)using the limit definition of the derivative.

A: Given f(x)=5x-1

Q: 4. Given f (x) =x' -12x +1. Use the second derivative test to determine the local extremum of f (x…

A: See the attachment.

Q: 6. Use the limit definition of derivative to find f'(x) for the functions below. (a) f(x) = /4r – 1…

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

Q: Let f(x)=1x−2 ; for what values of x , f(x) will be discontinuous?

A:

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

A:

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: 2 Find the derivative of the following function f(x)=2x-10x -8 using the limiting process a.…

A: The function is given by f(x) = 2x2-10x - 8 To evaluate : The derivative of the function using…