Indeterminate Form 12. lim tln 1+ X- 13. lim [w² In(4²)] 14. lim[e* +x] 15. lim[cos2y] yo* x0*

Q: 2-limx-o(x. secx.cscx)

A: To find the limit of the following.                                     limx→0 (x sec x csc x)

Q: 1. + x+1 lim -1 /-

A:

Q: 3n Find lim,→0 (1+ )'

A: Here,

Q: 1. lim 2x

A:

Q: 3. Find lim (x² + 3x – 18)/(x – 3)-

A:

Q: x-1-2 2) lim 1 1 Xー 2 2,

A:

Q: 2. lim (x - Inx)* x)² 2-0+

A: Here, the given limit is: limx→0+(x-ln x)x which is (-∞)0 form.

Q: 2-x+x* lim * 5x* – 3x

A: Explanation: Given that,  limx→∞2-x+x45x4-3x2 If we directly put the x limit, we get ∞∞ We will take…

Q: t -9 9. lim- -3 2t +7t+3 1 1 11. lim x-3

A: 9) limt→-3t2-92t2+7t+3=limt→-3(t-3)(t+3)(2t+1)(t+3)=limt→-3t-32t+1=-3-32(-3)+1=-6-5=65

Q: csc(6x) 7. lim x- csc(2x)

A:

Q: Sfsin(r – y kýyd . B. (i) Evaluate 00 sVx+1 lim (ii) Evaluate * 4Vx +3

A:

Q: 8+x-4x? Lim\ belowr → 0∞ V6+x²+7x* O a. -4/7 O b. 4/7 O c. 4//7 O d. -4/7

A:

Q: x²-1 2. limx-1 1-x

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

Q: 3 lim (1+ 4 x2

A: Given thatlimt→∞1+3x+4x2x. The objective of the problem is to solve the given limit.

Q: 4.lim 1252x-7+2 Sーズ 5. lim e*+1 X-4

A: Let's find.

Q: (4+ 43) (x + 43) -(16 + 43)x limy→ -43 limx. x + 43

A:

Q: d) (x+27) -3 X lim-

A:

Q: .Using &-8 definition show that x3 – 4 lim x→2 x2 + 1 - 4 4 - + in

A:

Q: x2/3 16 18. lim

A: Given that: limx→64x2/3-16x-8

Q: 2x³ – 3x³ + 7x-1 lim X-→+∞ 7x – xª + x² –3 2.x5 – 3x3 +7x6 – 1 lim 7x - x4 + x² – 3 X->-00

A: (a)     limx→∞       2x5-3x3+7x-17x5-x4+x2         we take commom x5             limx→∞…

Q: 2x a. lim x-+3" X - 3

A: limit

Q: 2. Evaluate lim (5x - 2 x+3.

A: To evaluate the limit: limx→∞5x-2x+3 Solution: We know that, limx→afx-gx=limx→afx-limx→agx Using the…

Q: 1. lim x-2 (2x + 3)

A: 1. To find the given limit limx→ 22x+3

Q: x +1 13) lim x-1 x +1

A: Given:              limx→-1x3+1x+1 Simplify: x3+1x+1 Apply: a3+b3=a+ba2-ab+b2…

Q: x2" lim; 2" 02

A: When limit is of the form 00or ∞∞ (Indeterminate form ) then L Hospital's rule is applied , In L…

Q: 3x(x - : lim Tx - 1| X1+

A: Replace the value of the limit and x.