7. Find the limit, if it exist x² +2 a. lim xV9 - x? C. im b. lim * x-1

Q: Find the limit (if it exists). If it does not exist, explain why.

A: first we factor the denominator

Q: Use the precise e-d definition of limit to prove that lim (13 – 4x) = -3.

A: Given data:     The given limit of the function is: .   For ? >0, the expression for the limit of…

Q: Lim 9. x + 4

A:

Q: lim 1+ 3x = -5 X--2

A: To prove: limx→-21+3x=-5 Solution: Given, limx→-21+3x Here function f(x)=1+3x is a linear function…

Q: Evaluate the limit: lim (8z – 52)

A: Put Z=-1

Q: Evaluate the limit: lim 5x 6x %3D

A:

Q: Find the one-sided limit (if it exists).

A: Given We have to evaluate given one sided integral.

Q: 5. Use the precise definition of a limit to prove that: lim +23D3

A:

Q: Determine the infinite limit. (а) lim (x – 3)5 x→3-

A:

Q: Calculate the limit lim 2√(x-4) / (x-4) As x goes to 4

A:

Q: 3. Use the precise definition of a limit to prove lim(9 – x) = 5

A:

Q: use definition of limit to show:   lim    (4x + 1) =13 x->3

A: The definition of limit:

Q: Find the limit, if it exist の十2 lim

A:

Q: lim 4x + 3 = 7

A: To provelimx→14x+3=7

Q: Evaluate the limit. 6. lim xtan

A:

Q: Use the ε- definition of limit to prove...

A: let the value of the ∂ be ∈3 thus the limit limx→2(3x-2)=4 is proved when the expression…

Q: Evaluate the limit: lim 5 = x → 2

A:

Q: Determine the infinite limit. lim X→-7 X + 7.

A: Given,       limx→7-( x + 6x + 7 )

Q: By using the e –- N definition of limits, prove пз — Зп - = 1. lim п00 п3 — п — 2

A:

Q: a) Prove the statement lim +3 by using the ɛ, ô definition of the limit x→6 4

A:

Q: Find the following limit or state that it does not exist. lim (-3x+4) X-1

A:

Q: Find the following limit or state that it does not exist. lim 7 X -2

A:

Q: Use the Basic Limit Laws to evaluate:

A: We have to evaluate the following limit: limx→2x3+5x+7

Q: Find the one-sided limit (if it exists).

A: we have to find the value of the one sided limit(if it exists): limx→2+xx-2…

Q: Evaluate the limit. lim (4x)/

A:

Q: Find the one-sided limit (if it exists).

A: Given :                       f(x) = limx→2- 1x2-43

Q: Evaluate the limit 1 lim x--3 (x + 3)²

A:

Q: Use the precise definition of limit, without using any of the limit laws, to prove that lim (2x + 10…

A: The equation of the function is limx→32x+10=4

Q: Evaluate the limit. lim (1 – 5x)

A: Given ,  limx->0 (1-5x)1/x Putting x = 0 , =>  = ( 1 - 5*0)1/0 = 1∞ As f(0) is in the form of…

Q: Determine the limit, if it exists. lim 5 (x -7) X→3

A:

Q: Find the limit if it exist.

A:

Q: Evaluate the limit, if it exists.

A: The given expression is limx→-2x+2x3+8

Q: Find the limit, if it exists

A:

Q: Find the one-sided limit (if it exists).

A:

Q: Calculate the limit, if it exists, 5 lim x→7 (7-x)

A: On solving this we will get

Q: Find the limit, if it exists. lim (7 + x- 00

A:

Q: Evaluate the limit: Lim X--3 (2-√x² +100 x + 3

A:

Q: 4. Use left and right hand limits to determine if the following limit exists, 22 + 2x - 3 lim 2-3

A: To find:- Use left and right hand limits to determine if the following limit exists

Q: | | lim 10 - x 10 - x X - 10

A: Now left hand limit is, and right hand limit is,

Q: Evaluate the limit lim x²sin 4x2

A: We can use substitution In order to solve this problem.

Q: Find the limit.

A: Given: limt→∞ 2-t2

Q: Find the following limit or state that it does not exist. lim 1 X-3

A:

Q: Evaluate the limit, if it exists. lim (1/4+1/x)/(4+x) x--> -4

A: The given expression is,

Q: Prove the statement using the e, 8 definition of a limit. (--) 4 lim -5 - - x 5 x→10 ||

A:

Q: Evaluate the limit, if it exists. (If 1-t lim 1- VE

A:

Q: Find the limit. 54) lim (lnx)/x X→∞

A: We need to find limit.

Q: Find the limit or show that it does not exist lim 212 + 3t – 5

A:

Q: ) Use the definition of limit to verify lim -3x +2 = –10 x→4

A: