Let ƒ(x) = (3x - 1)/x. Make tables of values of ƒ at values of x that approach c = 0 from above and below. Does ƒ appear to have a limit as x→ 0? If so, what is it? If not, why not?

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: Let (7z 2x2 for I<0, 8z2 + 7x for r20. f(1) = According to the definition of the derivative, to…

A: Given : Derivative any function is as follows let   f(x)= xm

Q: For the continuous function f(x), if f’(-4) does not exist, then x=-4 is a critical point.

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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: if f(x) is a continuous function at x = -6 * = 0, then a 1- cos4x x2 If f(x)= { a x = 0 r>0 16+Vx-4

A: a= 8.   See the attachment for the complete solution.

Q: For the function given by q (x)= x² + 2x+1, use the limit definition of the derivative to compute…

A: Definition of the Derivative:        The derivative of f(x)  with respect to x is the function f'(x)…

Q: Find a value for the constant "a" that will make the function f(x) continuous. f(x) = { ax- if xs2…

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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: Let f(x) = V13 – x. Compute f'(4) using the limit definition f'(4) =| Find an equation of the…

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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: Let f(x) = 2x2 - 3x - 5. Show that the secant line through (2, f(2)) and (2 + h, f (2 + h)) has…

A: Definition used -                   The slope of secant line -…

Q: evaluate the limit:  limit of the square root of 1+t - square root of 1-t / t as t approaches 0

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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: If f(z) = V1+ 4z, find f'(1), using the definition of derivative. f'(1) is the limit as z1 of the…

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Q: If functions ƒ(x) and g(x) are continuous for

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Q: Let            fn(x) = nx/1 + nx2  (a) Find the pointwise limit of (fn) for all x ∈ (0,∞).

A: Given : fn(x)=nx1+nx2; To find the point wise limit of this function for given values of x: We have…

Q: Let f(x) = V17 – x. Compute f'(8) using the limit - definition f'(8) = | 8 Find an equation of the…

A: To find the derivative of f(x)=(17-x)1/2 using limit definition and also obtain the equation of…

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

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

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

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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: Find the limit as x approaches c of the average rate of change of the following function from c to…

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Q: The limit of a function y = f(x) as x approaches c isdenoted by the symbol________

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Q: f(x, y) = e¬aY sin(x + y) (г, у) —> (1, -1). as

A: We will plug the limits in function to find limit of function

Q: 1 -1 lím (x,y)→(0,0) tan x² + y?

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Q: Let f(x) = 3x² – 5x + 1 f(x+h)-f(x) (a) Find f'(x) using the limit definition of derivative. That…

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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

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Q: The limit of f(x) = sin(x) as x approaches t is O T/x n/2

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Q: Find f'(a) using the limit definition for 1 f(x) = V6 – 5x -

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Q: Let f(x) = 3√(x + 1) − 4 = (x + 1)1/3 − 4. Use the limit definition of the derivative to show that f…

A: Consider the given function: fx=x+13-4=x+113-4 Vertical tangent at point indicates that at that…

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

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Q: dy -) using definition with limit of the following: dr 4. Find the differentiation (- y = /2x + 1.

A: We need to find the differentiation of y=2x+1 using the definition of limit. Now, according to the…

Q: Q3) If the function (2x + 1 +2 x > h) XSh f(x) having limit at x = h. Find the value of h. Q4) f(x,…

A: Our objective is to solve the above questions.

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

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Q: Find: a. f (0) b. limit of f (x) as x approaches 2 from the left c. limit of f (x) as x…

A: We have to find

Q: For every continuous f:[0,+0) →R _function , if a>0 2fx'f(x*)dx =[ xf(x)dx Demonstrate that this…

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Q: Find the limit of f(x) = as x approaches co and as x approaches - oo. 4 -

A: Given,          fx=-4+2x4-6x

Q: Let F(x) = | 3e“ dt. Find lim F(x) if it exists. If the limit does not exist, explain why. x→0

A: see below the answer

Q: find the limit of f(x)= ((x+h)^3-x^3)/h as h approaches 0

A: SOLUTION-

Q: Find the limit as h approaches zero of f(x)=[1/(x+h)^2-1/x^2]/h

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Q: F(x) Let F(r) = | 3e" dt. Find lim if it exists. If the limit does not exist, explain why.

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Q: Does the existence and value of the limit of a function f(x) as x approaches a ever depend on what…

A: Yes, existence and value of the limit of a function f(x) as x approaches a depends on what happens…

Q: If ƒ(x) is continuous [-00,b]then on ſf(x)dx= lim [ ƒ (x)dx а. a a

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

Q: Suppose that f (x) is a continuous function. 3 If | f(x) dx=5, then what is the value of z - f(x)]…

A: Given, ∫13f(x) dx =5Now,∫13[x -f(x)] dx= ∫13x dx -∫13f(x) dx =x2213 -5…

Q: d. Use the limit definition of the derivative, f (x) = lim f (x+h)-f(x) 1 +h)=j, to prove that VT =…

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Q: Find the limit of (x3+x2)1/2sin(((2)1/2pi)/x) as x approaches 0

A: To find

Q: (b) FIND the value of c, so that f(x) = {cx – 1, x< 0 lx² – 1. x 2 0 is continuous everywhere.

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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: Find the limit as x approaches infinity of the function V2 – x2 h(x) х3 — х + 1

A: Given:  h(x)=2-x2x3-x+1h(x)=x2 2x2-1x31x3-1x2+1  (Taking highest power of x in the…

Q: Compute the limit of the function at −1 AND determine if the function is continous at 1. f (x) = {…

A:

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.