d. Use the limit definition of the derivative, f (x) = lim f (x+h)-f(x) 1 +h)=j, to prove that VT = 6. h→0 dx

Q: Use the limit definition to compute f '(a) and find an equation of the tangent line. f(t) = t-3, a =…

A: Given: ft=t-3  ……1 a=1  ……2   To find: f'a and equation of tangent line

Q: Use the limit definition to compute f '(a) and find an equation of the tangent line.

A: Answer: f'(-2)=-1

Q: compute f ' (a) using the limit definition and find an equation of the tangent line to the graph of…

A: Plug x=4 to find f'(4) Answer: f'(a)= -1/16

Q: Compute the right-hand and left-hand derivatives as limits to show that the functions are not…

A:

Q: Use the following definition of a derivative fla=lim f\x-f(a) x-- a x-a To find fa), where f x=x°-…

A: Given, f(x)=x3-2x  To find f'(a).  Solution: f'(a)=limx→af(x)-f(a)x-a      =f(a)-f(a)a-a=00

Q: Is the limit of f (x) as x approaches c always equal to f (c)? Why or why not?

A: To prove :                   The limit of f(x) as x approaches c always equal to f(c). Answer :…

Q: Compute the right-hand and left-hand derivatives as limits to show thatthe functions in Exercise are…

A: The definitions of the left-hand side derivative and right-hand side derivative can be used to show…

Q: Let f (x) = xex . Use the limit definition to compute f'(0), and find the equation of the tangent…

A: Given: fx=xex We know that f'x=limh→0fx+h-fxh…

Q: compute f'(a) using the limit definition and find an equation of the tangent line to the graph of f…

A: f(x)=x3, a=-2

Q: compute f ' (a) using the limit definition and find an equation of the tangent line to the graph of…

A: Given f(x)=x2-x The limit definition for derivative of a function is given as: Using the above…

Q: In the given equation as follows , determine whether the statement is true or false. If it is false,…

A: f is continuous function on [0,∞) and ∫0∞f(x)dx diverges

Q: Show that the function f(x, y) x4 + y? has no limit as (x, y) approaches (0,0).

A: Note: Since we can solve at most one problem at a time, we have solved the first one. Kindly…

Q: Fill in each blank so that the resulting statement is true.

A: We know that the derivative of f at x, denoted by f'x, is defined by limh→0fx+h-fxh provided that…

Q: Use the limit definition to compute f '(a) and find an equation of the tangent line.

A:

Q: use the limit definition to compute f'(a) and find an equation of the tangent line. f (x) = x3 + x,…

A: For a function f(x) the limit definition for derivative at x=a is f'(a)=limh→0f(a+h)-f(a)h. The…

Q: Use the limit definition to compute f 1 (a) and find an equation of the tangent line. f (t) = 2t3 +…

A: Given: f(t) = 2t3 + 4t, then f'(t) = 6t2+4.   Then f'(4) = 6 * 16 + 4 = 100   At t = 4, f(t) = 6 *…

Q: Use the limit definition of the derivative function to find 4 x2]. dz Which of the following sets up…

A: The objective is to use the definition of limit to find the derivative.

Q: Suppose f is continuous on [0, 1]. What is lim n→ ∞ 1 S fo 0 f(x) dx?

A:

Q: Computing the derivative of ƒ(x) = x2 ex

A: Consider the given function fx=x2ex

Q: Evaluate f x2 dx using the limit defintion of the definite integral.

A:

Q: Let f(x) be a continuous differentiable function that f(x)- 4 satisfies lim =D5 %3D x3 x-3 Which…

A:

Q: lim, - f{x)= 0, then f(x)dx diverges Select one: O True False

A: When the limit exist or equal to 0 then the series is convergent otherwise divergent.

Q: Use the limit definition to compute f '(a) and find an equation of the tangent line. f (x) = x3 + x,…

A: Anwer: f'(0)=1

Q: Use the limit definition to compute f' (a) and find an equation of the tangent line. f(t) = √(t2 +…

A: Consider the provided function, ft=t2+1    a=3 Find the limit by the definition to evaluate  f'a and…

Q: Use the limit definition to compute f 1 (a) and find an equation of the tangent line. f(x) = 2x 2 +…

A: Given:                fx=2x2+10x,     a=3 Find: f3+h and f3 f3+h=23+h2+103+h…

Q: Use the limit definition of the derivative to compute p′(t) if p(t) = 2t^2−3t+ 1.

A:

Q: Use the definition of the derivative (that is, f'(a) = lim sec(x) da to compute h+0

A:

Q: Let f(x) = V9 – 2x. Find f'(x) using the limit definition of the derivative.

A: To find f'(x) by definition f(x)=√(9-2x)

Q: Which of following limits is the derivative of g(x) =5x at =2? 10 – 5h lim h 10 + 5h lim h>0 h 10 +…

A:

Q: Use the limit definition to compute f 1 (a) and find an equation of the tangent line. f (x) = x +…

A: For a function f(x) the limit definition for derivative at x=a is f'(a)=limh→0f(a+h)-f(a)h. For a…

Q: compute f'(a) using the limit definition and find an equation of the tangent line to the graph of f…

A:

Q: given f(x) = (2x+1)/(x+3), use the limit definition to find the tangent line to graph of f(x) at x=0

A:

Q: We can now evaluate this limit to conclude that the derivative is as follows. 1 a1/3 + a2/3) f '(a)…

A: We have to evaluate limit

Q: Use the limit definition to compute f 1 (a) and find an equation of the tangent line. f (t) = 2…

A:

Q: If ƒ' is continuous on [0, ∞) and lim→∞ f(x) = 0, show that I p'(x) dx = = -f(0)

A: First we will integrate then put limit

Q: Find the limit of f(x) as x approaches 2, where

A: fx=1,  x≠20,  x=2

Q: . Use the limit definition of the derivative to show that if f(x) = +, then f'(c) = = very c e R,…

A:

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

A:

Q: Let f (x) = In(x + 2). Use the definition of the derivative and your now expanded knowledge of…

A:

Q: Use the limit definition to compute f '(a) and find an equation of the tangent line.

A:

Q: Use the limit definition to compute f '(a) and find an equation of the tangent line.

A:

Q: . Is f(x)= Vx + 1 continuous at x == -1? Yes, because all functions are continuous No, because the…

A:

Q: Let f (x) = xex . Use the limit definition to compute f ,(0), and find the equation of the tangent…

A:

Q: Let f(x) /36 – x. Compute f'(0) using the limit definition | f'(0) = %3D Find an equation of the…

A: Solve the function and find the equation of the tangent line

Q: Suppose that f(x) is a continuous function on the interval [0, T] . If f(x)=(sin x)ª for 0<x<T, then…

A: we have to find the value of given function. the solution is following.

Q: If f' is continuous on [0, ∞) and limx→∞ f (x) = 0 , showthat

A: Given, If f' is continuous on the interval [0,∞) and limx→∞f(x)=0 show that, ∫0∞f'(x)dx=-f(0)

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.