Is P(x) continuous at x= 3? O No, because lim P(x)+ P(3). x-3 O No, because lim P(x) does not exist. x-3 O Yes, because lim P(x) exists, P(3) exists, and lim P(x) = P(3). X-3 X-3

Q: Given that lim f(x) = -1, lim g(x) = - 3, and lim h(x) = 4, find X 2 x2 lim [f(x) • h(x)] g(x) f(x)…

A: limx→2f(x)=-1, limx→2 g(x)=-3, limx→2 h(x)=4

Q: Find lim x→∞ h(x), if it exists. f(x) = 9x2 + 2x + 7   (a)     h(x) =  f(x) x lim x→∞ h(x) =

A: We are asked to find the limit of the function.

Q: Given (x + 1, f(x) = {Vx + 3, 1 4 Tentukan: Determine. (a) lim f(x) x→1-° (b) lim f(x) x→1+' (c) lim…

A: To evaluate the given limits

Q: Determine whether the function x2 + 2 x > 2 f(x) = x = 2 is continuous at the 4х — 2 x < 2 given…

A: First of all we will find the left hand limit at X equal to 2 and then find the right hand limit X…

Q: Given x +1, f(x) = {Vx + 3, 1<x<4 0<x<1 7, x24 Tentukan: Determine. (a) lim f(x) X-1 (b) lim f(x)…

A: To find limits of the given function f(x)

Q: Find the limit, if it exists.

A:

Q: Find the limit. lim x→0+ (- 7lm a)" In x

A:

Q: The value of the limit lim a) 0 b) 1 c) d) ∞ 1 X x-0 sin x sin x 6 is

A:

Q: f(x+h)-f(x) In evaluating lim h-0 in f(x)= x² -1, which is the first step? h

A:

Q: lim[f(x)+ 4g(x)]

A:

Q: _15. What is lim f(x)? X-4 A. 0 В.1 С.2 D. Does Not Exist

A: Given: Following graph is given. To Find: 15. limx→4fx=?

Q: 6. Find the limit of f(x) = -- 10 as x approaches co and as x approaches - c lim f(x) = X00 (Type a…

A:

Q: Given f(x) = 4 – x² and g(x) = væ +1, find lim g(f(x)). %3D O 2 does not exists O none of these

A:

Q: ind the indicated limit, if it exists. (If an answer does not exist, enter DNE.) lim x→∞  x2 x2 − 3

A:

Q: For the function f(x) (X^2-3 if -3 ≤x2 C) is f continuous at x=2? D) does lim f(x) exist at x->4^-?…

A:

Q: Find lim h(x), if it exists. f(x) = 6x2 + 2x + 9 f(x) (a) h(x) = lim h(x) = x→の f(x) (b) h(x) : x2…

A:

Q: Find the limit. lim X-2 x+2 O 1/2 -00 O Does not exist

A: Answer is limit does not exist

Q: Find the value of the limit: 3x -9x e -e lim In(1+x)

A: Using limit to find the value of given function

Q: Is there a real number a such that 3r + ar + a+3 lim --2 r+x + 2 exists? If so, find the value of a…

A:

Q: lim (sin?x x-0 x2

A: We use L-Hospital Rule to evaluate this limit.

Q: Find the limit. lim x-2/In x X x-0+ O -2 O e?

A:

Q: A = lim R, = lim [f(x1)Ax + f(x2)Ax+.+ n-00 x< 10. Using the above definition, determine whic

A:

Q: When proving the limit lim(x² + 4x - 1) = 11, and e > 0 is given, what is an appropriate choice for…

A:

Q: -1, x0 c. lim f(x), where f(x) =

A:

Q: lim f(x) = 81 (a) VF(x) (b) [3f(x)] (c) [f{x)]²

A: Using rules of limits.

Q: Evaluate the limit given

A:

Q: If f(x) < x² for all æ E R and lim f(x) exists, then what can be concluded about lim f(x)? a. lim…

A: we have to find the following

Q: Determine the limit algebraically, if it exists x3 + 12x2 – 5x lim 5x O -1 O 5 DNE

A:

Q: Evaluate the limits. |7x| f(æ) = { x # 0 x = 0 Enter DNE if the limit does not exist. a) lim f(x) =…

A: According to question,Given Function,fx = 7xxx≠00x=0

Q: 2. Calculate the limit algebraically. x-11 lim O -1.8 03 -0.6 O 1.8

A: Given

Q: If A(t) is continuous at m, then what is the value of lim A(t) ? t-m If h(f) is continuous at G,…

A: If A(t) is continuous at m, then limit t goes to m should be equal to value of function A at m i.e…

Q: Given that lim f(x) = 2 .lim g(x) = -4 .lim h(x) = 0 Find the limit lim[h(x) – 39(x) +1]

A:

Q: Consider a function x-1 if x 1 (a) Find lim f (x) if it exists. If it doesn't exist, explain why.…

A:

Q: Evaluate the limit given

A: Given:

Q: Shone that lim g (x,yJ-p (0,0) does not exist,

A: According to the definition of limit, we have

Q: 3 (а+h)2-За? Algebraically calculate the exact limit: lim h→0 h

A:

Q: 1. Prove, using the e-6 definition of limit, that: (a) (b) lim lim_2²+1=2 24-1 x³+x²+x+1= 4.

A: Limit

Q: nd the limit. e3x p-3x lim x→0e3X - e-3x

A: on solving this we get the

Q: 44. Prove that if lim f(x)= L #0 and lim g(x)= 0, then the limit lim 8(x) does not exist.

A: Given: limx→cf(x)=L≠0 and limx→cg(x)=0 To Show- limx→cf(x)g(x) doesnot exist. Theorem- if limx→au(x)…

Q: Find the limit of f(x)

A: Given information

Q: Find lim 4(x) (x) / X-0 x 2. Prove that B(m, n)

A: Limit of the bessel function

Q: 2. a) Find lim g(x), lim g(x) and lim g(x) x→1- x→1+ x→1 b) Find f(1). c) Is g continuous at x = 1?…

A: Follow the procedure given below.

Q: Given that lim f(x) = 4 X-3 lim g(x) = -5 X-3 lim h(x) = 0, X-3

A:

Q: Given that lim f(x) = 2 ,lim g(x) = -4 ,lim h(x) = 0 %3D %3D xa xa Find the limit lim[h(x) –…

A: Limit evaluation: 1) limx→cA(x)+B(x)-C(x)=limx→cA(x)+limx→cB(x)-limx→cC(x) 2)limx→aag(x)=alimx→ag(x)

Q: Consider g(x)=−7x3+7x2+9. a) limx→0−g(x)= b)limx→−1−g(x)= c)On what interval(s) is g(x)…

A: It can be solved using the limiting definition of continuity

Q: 2. Evaluate the limits numerically. x-1 a) lim x-1 vx+3-2 x² +3x+2 b) lim x--1 x2-x-2 cos(x)-1 c)…

A:

Q: With lim f (x) = +o and lim h(x) = -∞ for any a that x→a' x→a is real number, which of the ff. is…

A:

Q: Find the limit of f(x) = 6 - 2 as x approaches o and as x approaches - o. lim f(x) = %3D (Type a…

A:

Q: x² – x + 1 1 - (c) lim x→1 x + 1 2 using definition of the functional limit

A: We can prove the statement as below using definition of limit

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.