The limit below represents the derivative of some function f(x) at some number a. 2(1 + h)° – 2 lim h h→0 State the function and the number: f(x) =

Q: V1– 3x, if x -1 2x +1 Show that f is continuous at x = -1 is differentiable there by computing the…

A: See below the calculation

Q: Write down the limit definition of the derivative f'(x) and USE IT to find d/dx(1/x)

A: Write down the limit definition of the derivative f'(x) and USE IT to find d/dx(1/x)

Q: 1. Use limits to find the derivative of the following function at the point a = -1. 1 2x + 1 f(x)= =…

A: We have to find derivative

Q: Use the definition of the derivative, f'(x) = lim z+h)-(2) to findf' (x) where f(x) = x³ +1. h→0 O…

A: fx=x3+1

Q: 10 at x + 4 x = 0 using the limit definition of the derivative. Find the derivative f' (0) of f(x) =

A:

Q: 2) The limit below represents the derivative of some function f(x) at some number a.…

A:

Q: 5a) Using the formula man = lim+)=/G2 determine the derivative/ slope of tangent for h→0 the given…

A:

Q: Compute the derivative function f'(x) algebraically. f (x) = 3x2 +x lima 0 (6z + 3h + 1) = 1 limp 0…

A: Given Data: Function: f(x)=3x2+x For f(x+h), Substitute x+h for x in the given function.…

Q: Is the following statement true or false? The function g(x) = x|x| has a derivative at x = 1. Choose…

A:

Q: If h =z-2, which of the following best describes the derivative of f at r /(z+h)-f(z) 1. lim 0 I.…

A: Given that h=z-x Derivative of f at x

Q: I. Find the derivative of the following functions using the limit definition. Show your solutions. (…

A:

Q: 5. (a) Use the limit definition of the derivative to find the derivative of f(r) = /5I+1. %3D

A:

Q: The limit cos(x) +1 lim x – 9T represents the derivative of some function f(x) at some number a.…

A: In the given question, f(x) is cos(x) and a is 9π

Q: Let f(r) = v5x +2. Using the definition of derivative at a point, %3| a. enter the expression needed…

A:

Q: 8. Given that f(r) is continuous at r = 0, is f(r) differentiable at z = 0? (If yes, find f(0) using…

A:

Q: 1 f(x) x – 2 Use the limit definition of the derivative to find (1) f' ( – 1) = (ii) f ' (0) = (iii)…

A:

Q: The limit cos(x) – 1 lim с — 4т represents the derivative of some function f (x) at some number a.…

A: This question is about finding derivative about a point .

Q: I. Find the derivative of the following functions using the limit definition. Show your solutions. (…

A:

Q: The following limit is the derivative of a function f at some number a: V2 +h-V2 f'(a) lim 0-4 h (a)…

A:

Q: The limit lim h→0 ((√ 144 + h) – 12)/ h represents the derivative of a function f(x) at a number a.…

A: Given,           limh→0144+h-12h represents the derivative of a function f(x) at a number a.

Q: II. Compute the right-hand and the left-hand derivatives as limits to show that the following…

A: Given,

Q: Consider the function f(x) = Va, x > 0. Use the limit definition of the derivative to compute the…

A: Given,           The function is fx=x , x>0We know that,           The derivative of the function…

Q: Suppose g: IR - IR is a differentiable function with bounded derivative, Fix e> 0 , and define flx)…

A: to show f is one one we will show that for  x1 not equals to x2 , f(x1) is not f(x2)

Q: Let y = f(x) be a differentiable function. If the derivative of f is zero at x = a, then the…

A: Given statement : Let y=f(x) be a differentiable function. If the derivative of f is zero at x=a,…

Q: Find the derivative of the function using the slope limit formula. 1 y= 3-х 1. y=(3x+1)2 2. 1 y= 1…

A: Note : As per our company guide lines, we are supposed to answer only one question. Kindly post…

Q: [8] Use the definition f(a +h) – f(a) f'(a) = lim h-0 h To find the derivative of the given function…

A: Given: So,          f'(2)=limh→0f(2+h)-f(2)h       =limh→ 012+h-12h       =limh→ 0-12h+2       Plug…

Q: Given f(x) = 3 find f'(x) using the limit definition of the derivative. - f'(x)=

A:

Q: Find the derivative of the function by the limit process. g(t) = t³ +7t g'(t) =

A: We have to find derivative

Q: Find the derivative of the function by the limit process. g(t) = t³ + 6t g'(t) =

A: We can find the answer as below.

Q: Use the limit definition of the derivative to find a formula for f'(x) if f(x) = (g(x))², assuming…

A: Given  The function is f(x)=g(x)2  where g(2) =-3  and  g'(2) = 4 .   limit definition of derivative…

Q: E. Set up the limit definition for finding the derivative of y = sin x.

A: Givne that  y=sinx  From the limit definition find the derivative of y=sinx

Q: This limit represents the derivative of some function V16+h-2 f at some number a. State this f and…

A: Given limit as a derivative of the function limh→0(16+h)14-2h  we have to find the value of a and…

Q: 3. Let f be defined by f(x) = e* sin x. What is the slope of the line tangent to the graph of f at x…

A:

Q: The given limit represents the derivative of a function y = f(x) at x = a. Find f(x) and a. lim [2(4…

A: It is given that limit representation of the derivative of a function y = f(x) at x = a,…

Q: a) Find dx of the function y = (x+1)²using the limit definition of the derivative. b) What is the…

A:

Q: Let F(x) = L te“ dt. Use the definition of the derivative to find F'(x). Note that, for a differen-…

A: To find F'(x)=?

Q: Let f(x) = 4x + 11a – 5. %3D f(x + h) – f(x) Using the definition of derivative, f'(x) = lim h enter…

A:

Q: Use the limit definition to calculate the derivative at z = a of the linear function k(z) = 10z +…

A:

Q: The limit below represents a derivative f' (a). Find f(x) and a. sin ( +h) – 1 lim h-0 h f(x) = a =

A:

Q: II) By using the limit definition of derivative, prove the identity J dzf(2)8' (2) = - / da f…

A:

Q: Use f'(x) = lim **n)=l to find the derivative at x for the given function. h h-0 s(x) = 8x +7 s'(x)…

A: A function is a relation which maps each value in its domain to exactly one value in its range.…

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

A: Given :  f(x) = √( x-1)

Q: 24 The following limit gives the derivative of a function f(a) at a point zo: √8th-2 lim h 0 h

A:

Q: Take the function (e 1>0 f(x) = %3D Compute its derivative at all values of x € R. Is f'(r) itself…

A: Given:   To determine: differentiation of f(x) and differentiability of f'(x)

Q: 4. Consider f(z) = v9 – z. (a) Use the limit definition of derivative to find f(r). (b) Find the…

A:

Q: Define h(x) = x° sin(1/x) for x # 0 and h(0) = 0. Prove that h is differentiable at x = 0, and find…

A:

Q: Find the derivative of the function by the limit process. h(s) = −2√s

A: h(s) = −2√s

Q: Consider the function y = g(x)= -x² + 3x +2. Compute g(2). Use the limit definition of the…

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.