1- V1– x2 с) lim x→0 [without using l'Hospital Rule] x2 -1- x – a? d lim x→0

Q: 20. lim_ v3 – x x→3-

A: We have to find the limit

Q: 1-cos(0) lim 02 e-0 1 lim (1 + x)a x-0 If f (x) is continuous at a, then what is the value of lim…

A:

Q: Q:Prove that: Vi+x+x² -1. Lim- 12-2 cos x + lim x->T/4 sin(x - T /4) > log, 0.005

A:

Q: Solution of lim (Vx² +1 – x) is ... x→ 00 Tentukan lim (vx² + 1 – x) x→00 1. O 1 2. O infinite 3. O…

A:

Q: 4. Proof Prove that lim x"y" dx dy = 0. n→∞

A:

Q: 3-Vx+3 6. (10) Find lim analytically (if it exists). X→6 X-6

A:

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-coskx 2. lim kx = 0.

A:

Q: b) If x sin x 2 - 2 cos x hold for all values of x close to zero. Find limx0 xsinx ? 2-2cosx

A: Given, limx→0xsinx2-2cosx

Q: Q.1 Evaluate the limit x-3 sin2x 1) lim(2x2 +x + 1) 2) lim 2-9 3) lim x-1 x-3 x2-x+1 4) lim x+00…

A: We have to find limit

Q: Q2: (a) By using " L' Hopital rules "; Find the limits of ::- (1) limx¬(n/2)-(tan x)cos x (2) limx-o…

A:

Q: Lim as h approaches 0=[5e^x - 5e^(x+h)]/[3h]=

A: Given:  limh→0 5ex-5ex+h3h   Basic concept: The definition of the first principle of the…

Q: _11. If lim (x² +1) = 2, and x = 2.5, then x->-1 lim (x² + 1) is equal to. x-2.5 A. 5.25 C. 6.25 B.…

A:

Q: 1. Show that z³+y³ lim (x, y) (0,0) 1² + y² does not exist.

A:

Q: 1-coskx 2. lim = 0. kx

A: We have to find the limit of the function (1-coskx)/kx when x tends to 0 .

Q: lim x In(2x) x→0+

A:

Q: lim In (x°) x2

A: We have to evaluate the given limit.

Q: 3.lf limT(x--1) [(x^3+x^2-ax)] =1-a, then a= O a. 1. O b. 0. C. -1. O d. 1/2. 4-The equation…

A:

Q: (a) lim x→2 arctan(7-3x)-" 2х-4 4 (b) 10-e5x lim x→00 16-x2

A: See the calculation and explanation below

Q: lim (x,y)-(-3,4) (x³ +3x²y² - 5y³ +1)

A: Here we have given an expression with limit and we have to solve it. We have lim (x,y)→(-3,4) (x3 +…

Q: Find the limits in Exercise

A: limx22-1x

Q: H-w in limits 3-3- 2.21 9 iaam ) Lim. 1- CosC2K) Sin (24) 2 - メャ3 2) Lim x2x -3 3) Lim (X+4}-16

A:

Q: (3) Evaluate lim -(1+sin(4))t dt

A:

Q: Prove the limit doesn't exist

A: cc

Q: x2-x-2 2x-4 2sin(6x–12) 3(x-2) Sx-1 Let f(x)* ,g(x) • and h(x) Vz+2+1 a. Find lim f(x), lim g(x),…

A:

Q: lim (x,y)→(0,0) x3y is equal to----- x6+ y2 (a)1 (c)does not exist (d)-2

A: In the above problem, at the point (0,0) the function is not continuous. So, it is not possible to…

Q: a) lim- 1 3x +x+1 -x +5x b) lim f(x) where f(x)={ (4x xs2 3x x>2 sin 2x c) lim g(x) where 2+x < g(x)…

A: alimx→∞−x2+5x3x2+x+1Divide and multiply by x2limx→∞x2−x2+5xx2x23x2+x+1x2limx→∞−1+5x3+1x+1x2=−13

Q: (b) lim (r + 1) In x

A:

Q: (c) lim 1 In x x→0+

A: To find out the limit

Q: 1 d) limy-→0- e) lim,o (1+ r/n)" 1 f) lim→0 x +

A: L'Hospital Rule : If limx→af(x)g(x) is in the form 00 or ∞∞, then limx→af(x)g(x) = limx→af'(x)g'(x)

Q: 3x²+2x+1 Q1: Using the L Hopital Rule Evaluate: lim x→0o 5x2+3x+3

A: Given: limx→∞3x2+2x+15x2+3x+3  ……1

Q: Q3 :(A): By using " L' Hopital rules "; Find the limits of: 1 (1) limx-o[: 1-cos x 2 sin²x (2)…

A: We have to find the limit using L Hospital rule.

Q: determine the limit limh→0[(x+h)2-x2]/h by treating x as a constant. determine the limx→0cos(2x)/x…

A:

Q: 2. If lim x, = 1 and lim yn = 0, then it is possible to formally prove that lim(x, – Yn) = 1.

A: (Solving the 2nd question as per our guidelines) Solution of 2: The statement is "If lim xn=1 and…

Q: 2. Show that lim (x,y)→(−1,0) (x + 1)² sin y (x + 1)4 + y² does not exist.

A:

Q: 5. Show that lim –nx² e dx = 0.

A:

Q: 399. [T] lim e(x - 1) x-1 x-1

A:

Q: 1 + x +1 1 h 4 -2 (a) Lim–1 (b) Lim h→0 V5h + 4 – 2 X-0 X 5 t3 – 1 (c) Lim- = 3. t→1 t-1

A: (a) We take L.C.M. in the numerator and cancel the common terms in numerator and denominator. Then…

Q: Show that lim (x,y) → (0,0) 12 √16x +9y¹ 4x²+3y does not exist. Please show a complete solution.

A:

Q: lim (1,4) (0,0) x2 + y2 Prove that

A:

Q: V4 - x2 0sx<2 lim f(x), where f(x) = < 2 9) x-4" 2 sx<4 x = 4 B) Does not exist A) 4 C) 2 D) 0

A: f(x)=4-x20≤x&lt;222≤x&lt;44x=4

Q: 1 Prove that lim dx exists and find its value. (1+x?)" 1/2

A:

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

A:

Q: 2 In(x) c. limx→1 1-ex-I d. limr¬0 sin(x)-x cos(2x)-1

A: We can answer both the question as below.

Q: -x + 1,x 2 0 Let f(x) = {x² + sin x -,x <0' (a) Find left-hand and right-hand limits as "x"…

A: Consider the given information:

Q: lim aVx + 3 – b = 1, x - 1 Score А. 4 E. 1 В. 2 С. 1 4 -IN-IA

A: We can make it easier for you.