a) lim e2/(x-5) x→5-

Q: 1-z = ? What is lim %3D !- 2!- -2

A: In order to evaluate the limit of a function f(x) at certain point a then replace x by a to get…

Q: In x? c) lim- X-0 cotx2

A:

Q: lim (In(x))½ ?

A:

Q: lim In x X-→ 0+

A:

Q: lim at e -

A: Find the limit when x tends to 0

Q: prove limx->a 1/x = 1/a with epsilon-delta definition

A: We need to prove the given problem using the epsilon-delta definition.

Q: x + tan x 2? — 5х — 14 - (а) lim x0 3x + 4x² (b) lim (Do not use L’Hospital rule in part(b)) x7- x2…

A: Using rules of limit's.

Q: 1 Use l'Hopital's rule to evaluate lim 1+0+ \I In(1 + x),

A: Question is solved.

Q: lim In(r) - 0t

A: Consider the given limit

Q: 10 Find lim x12s 3. X->- X -25 2 lim Jx +3 - 2 メ→」 O lim Sitx - -x 3. 1-X 2 X

A:

Q: 21: The final value of :* lim (In(x))?

A:

Q: 1) lim (1--)*

A: As per our guidelines we can solve only 1 question. The rest can be reposted.    In question  no 1…

Q: ze" – In(1+#) lim

A: To evaluate the given limit.

Q: 1 1 Use l'Hopital's rule to evaluate lim x→0+ In(1+x),

A:

Q: Hence calculate lim 1- an (x³)' In cos x

A:

Q: Prove that lim š +1) = 3 using the e-8-definition.

A:

Q: lim x In(2x) x→0+

A:

Q: lim (In w-

A:

Q: b- lim [In(cos(x))]= x->0

A: Given that:limx→0[ln(cosx)]x

Q: lim In (x°) x2

A: We have to evaluate the given limit.

Q: Find the limit.

A: We can find the limit of an expression by applying the limit point as value of the variable in the…

Q: Find the limit.

A:

Q: Using e – N description to prove that lim - = 0.

A:

Q: Find the limits

A: To evaluate the limit: lim1x2-4 (a). When x→2+. Evaluating the limit. limx→2+1x2-4=12+2-4=10+=∞…

Q: х —9 Determine lim V6 - Vx-3 x→9 |

A: HERE WEMUST KNOW ABOUT L'HOPITAL RULE

Q: ® Find Lim X->2 x¥ _ 2x² - 8 x² - 4 (2 ,X +2 Lim 3X X→3 X- 3 -3 X+3 O Lim © Lim t- fo -) ,X EO X+2 2

A: "Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: tan(x) Q1: limx¬n X-n is

A:

Q: lim (In x)

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Find lim *2 x -2 In(x- 1) by using the La'Hospital Rule.

A:

Q: 12-x-x 1- Prove that lim -7 %3D x-3 V6+x-3

A: our objective is to find the limit

Q: Use Squeeze Theorem to evaluate -2x lim e COS x x 00

A: Based on the squeeze theorem or it is also been called sandwich theorem we can evaluate the limit by…

Q: lim (In(x))* ?

A:

Q: (i) Evaluate In (1-z³) lim 2->0 sin (2z

A: We need to evaluate the limit If the value of the function after putting the limit is in the…

Q: • lim In (tanx) -Lーえ • Lim V9x* + ax 2 4x-1

A:

Q: of

A:

Q: lim cas z is nonexistent

A:

Q: 7) Show that lim = 1. 200 (z-i)3

A:

Q: lim In(10x) x-0t

A: To find the below right-hand limit.

Q: 5. Show that lim –nx² e dx = 0.

A:

Q: lim, S(x), given 7-4x. x < 1 S(x) = { %3D x² + 2 x 21

A: Given: fx=7-4x,  x&lt;1x2+2,  x≥1

Q: lim x in (It -)

A:

Q: 8. Find lim x² In x x→0+

A:

Q: f(x+Ax)-f(x), Ff(x) = v2x + 1, what is the lim Дх--0 Ax

A:

Q: Find the limit.

A: Given,

Q: 3. Prove lim 3x-7= 2 X-3

A:

Q: alignment at x² + x – 1 limx→ 2x2 — х + 1 has a horizontal at???

A: Topic = Limits

Q: 1. Prove using e-d definition. (d) lim (4x + 3) = 7 x→1 x2 – 9 = 6 - (e) lim x→3 x – 3

A: To prove the limit using epsilon-delta definition

Q: Use e-5 definition and prove that lim (2 5r) -6

A: Here we use basic definition of epsilon and delta .

Q: Q show that lim %3D メ→ 0-1

A: We have to show that limx→0.11x=10 L.H.S : limx→0.11x           =10.1               (plug in the…