9. lim Sin- X-) too lim In X メ→( Use Mean-Value theorem to find c X +2x-1 ; [o,i] xj[3,5] Use L'Hôspital vule to find the wmit lime tan tan 2X ×ーS○

Q: 5x' + 8x² lim Q3/ Find a) x→0 3x² – 16x?

A: To evaluate: limx→05x3+8x23x4-16x2. Solution: limx→05x3+8x23x4-16x2 On simplifying further we get:…

Q: 83. W = lim7→∞CV2 (}--T)RC + }e-27/RC) = cv² (} - 0+ 0) – }cv² %3D

A:

Q: 6) lim (x – Ln(x² + 1)) X - X→∞

A: Here I am attaching image so that you understand each and every step.

Q: How do I compute  limx→4(x^2−6x+8/x^2−4x)

A:

Q: 5. lim tan x cos y = 1 (x,y)→(,0)

A: To show :  lim(x,y)→π4,0tan x cos y = 1

Q: 7. et² -e-y² = }(e - e-1) lim %3D (x, y)→(1,1) x+y

A: To Determine: to prove  lim(x, y)→(1, 1)ex2-e-y2x+y=12(e-e-1) Given: we have a  problem based on…

Q: lim (Vx2 – x – x) X→∞

A:

Q: 60. lim xIn 2)/(1 + In x) X→ 00 62. lim (e* + x)'/x X→ 00

A: We will find the limits.

Q: If h(x) →5 as x→ 1 and k(x) → 0+ as h(x) k(x) X→ 1 ? x → 1, then what is lim L

A: solution:-Givenh(x)→5  as x→1k(x)→0+   as x→1

Q: 2-Lim メ→」 X'+ 3 X²-5

A: Our Aim is to evaluate the limit in the expression given below:-limx→1 x4+3x2-5 -(i)

Q: lim_(tan(u)) = U- -3T 2

A:

Q: 16. lim x¹/ x→0+

A:

Q: 19. lim (-1)"+' (") does not exist. n00

A: Given  The limit is limn→∞(-1)n+1n-1n

Q: 59. Does knowing that x*y? tan xy 3 ху tell you anything about tan¬ xy lim (х, у) —- (0,0) ху Give…

A: The limit of a function of two variables fx, y is L when x, y approaches to x0, y0 and we denote it…

Q: 8. lim,0 1-cos x 2x2 1 (a) 1 (b) – (c) 0 (d) ; (e) 1. -

A:

Q: 11. lim x csc 3 х X→0

A:

Q: 5. lim (e' +t)i =? t→0+ (a) 1 (b) 2 (c) e (d) e? (e)

A: Solution of the problem as follows

Q: 1.1) lim 1-у2х+1 1+ →-

A:

Q: tan (xy) = ? lim (х, у) ->(1,0) у + 2хy

A:

Q: 15) lim cos (2x)

A: Let fx=cos2x

Q: lim (8n² – 7n – 500) = – In³ -

A: The rational expression 1xq can also be expressed as 1xq=x-q. We know that limx→∞ 1x=0. We also know…

Q: lim,[-6(x - sin' x)( cscx)] CSC X

A:

Q: an(xy) 3D? 2. (х.у) -> (0,1) х"y+x tan lim (a) 0 (b) (c) (d) (e) 1 114 113 112

A: Given : lim(x, y) → (0, 1) tan(xy)x2y + x     To find the limit.

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: 5n³ + (–1)" -? 4n³ + 2 3 If y = lim n→∞

A: