(d) lim x/x

Q: a) lim -Vx+7 2-x x-2 b) lim x+1 Show your work

A:

Q: sec x -1 lim -

A:

Q: Guess the value of lim x 0 sinx/x

A: We try to find the limit by substitution  But 0/0 is indeterminate form.

Q: x2 +1 Can L'Hôpital's Rule be applied to lim x→1 2x + 1

A: To check if the L'Hospital's Rule can be applied or not, first we need to find the limit by directly…

Q: Evalugte lim(3x-1)/x Xー>○ X/2

A: The solution is :

Q: lim et- ハ→0 ¥

A:

Q: 4+ x lim

A:

Q: Find the lim x-->0 (x2-x)/(x2+x)

A: We have to find the limit                                      limx→0x2-xx2+x

Q: lim (х — Vx? + х

A: Consider fx=x-x2+x. Simplify the above function. fx=x-x2+xx+x2+xx+x2+x=x2-x2-xx+x2+x=-xx+x2+x

Q: lim, 1 f(x) = %3D

A: limx→a f(x) =L if and only if limx→a- f(x) = L =limx→a+ f(x) .

Q: find: a) Lim x4-1 x2 b). Lim 10x-3 SinX

A: We have to find the following limit      alimx→1x4-1x2-1       blimx→010x-3sinxx

Q: 32. lim x + x - 2 x2 - 1 2,

A:

Q: What is lim ? X-0+ x

A:

Q: lim f(x) = %3D x-8-

A: We can clearly see from the graph that, f(x) is discontinous at  x = -8  But, if we move slightly…

Q: Find the one-sided limit

A: Given that limx→π+ xcsc x. Compute the limit as follows.

Q: lim- x-0 X

A: Given :limx→05x

Q: (a) lim n-0 2 – ni x² – 4 (b) lim x + 4 x² – 4 (c) lim x – 2

A:

Q: Evaluate the limit.

A: Given:                     limx→∞e4x-1-4xx2 Dividing the numerator by highest power denominator:…

Q: eax lim x → 0 In(1+ bx) -ах e

A:

Q: (e) limVx ) lim -+(-1)") X-00 n→0 n n²-12345 x2 +9 (g) lim n +1 (h) lim x∞x3 +1

A:

Q: d- lim x+1 /V2x²+x+1

A: First take x common and then use l hospital's rule to find the answer.

Q: lim zx+xて Xー→3 メ-3

A: Apply L hospital rule

Q: ■ Find the limit.

A: Given- limx→12-xx-12 To find- The value of the above limit.

Q: tan(x) Q1: limx¬n X-n is

A:

Q: (x² - 3) Build a table to estimate lim x-0 sin x

A: Given expression is

Q: 2) Find lim f(x). X→1 f(x> X 2. 2.

A: here      limx→1- f(x)=1    and            limx→1+ f(x)=2 here                            limx→1-…

Q: Q \ Find the value of 8 > 0 that guarantee lim x-0 csc(1/x) = 0 in terms of ɛ?

A: Definition of limit: We know that, limx→af(x)=L               ...(i) For each ϵ>0, there exists a…

Q: lim sec x x-(-71/2)"

A:

Q: Evaluate:

A:

Q: lim,-1 f(x) =

A:

Q: x2 – 3x 4 - - Evaluate the limit: lim x → - 1 5х + 5

A:

Q: Find lim_f(x), if it exists. If it does not exist, explain why. X--4"

A: Follow the procedure given below.

Q: using L'Hospital's Rule, what is limx->1+ (1/x-1) - (1/lnx)

A: compute the limit as follows.

Q: lim tkx'-1 k is a constant ト

A:

Q: 1. Using L'Hospital's rule, evaluate lim(1 – x²).

A:

Q: Then Lim (x fCX)-5) ?

A: Given limx→24fx=12 We will find the value of  limx→2xfx-5

Q: Vz - vā lim х-а 11(х — а) xa

A: Given - Function  To Find - Limit of function

Q: B) By using (A), Find lim /-

A: limn→∞1n

Q: Find  lim x+8/x-1 as x approaches -2 approaches

A:

Q: b. lim -3 where c is some fixed real number. +x+c-2 x>e

A:

Q: x² 12x + 27 - lim x → 9 x – 9 -

A: limx→9x2-12x+27x-9

Q: 1) If lim f(x) = , what asymptotic behavior will be illustrated in the graph of f (x)?

A: 1) If limx→6-fx=∞, then the value of the function fx tends to infinity as x→6 from the left hand…

Q: 23 - Vx - 47 Find lim x+ 24 X→-24

A:

Q: x' -x+1 Evaluate (iii) lim 5x' +7 and show work

A: The given limit can be evaluated by taking x3 as common from numerator and denominator

Q: x2-6x+9 lim x->3 is equal to: x-3

A:

Q: 8(x) x -1 Find lim

A: Solution is given below

Q: Evaluate limx=0 (e-ax - e-bx)/x

A:

Q: Evaluate lim X→∞ ९+2 1 - x³ ( if necessary, using L'Hôpital's rule)

A: limx→∞ex21-x3Apply L-Hospital rulelimx→∞2xex2-3x2limx→∞2ex2-3x