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

Q: 20. lim_ v3 – x x→3-

A: We have to find the limit

Q: 4. lim xy (xy)-(0.0) v2-e-1

A: To evaluate limx,y→0,0xy2-exy-1 Substitute t=xy, then as x,y tends to 0,0 implies t tends to 0.…

Q: Calculate each of the limits in Exercises

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

Q: (2 -1) s lim z

A:

Q: (1 cosr)dt 1. limx-0 2x -?

A:

Q: 2.y lim (x.y)-(0.0) 12x- Show that does not exist. -1ly

A: We will show that limx, y→0, 02xy212x2-11y4 doesn't exist. One path: (along x=0)    limx, y→0,…

Q: Q4: A) solve: 1+xsin 1) lim- y0 1+xcos sin 2) lim -2m 20-4

A: Note: We are entitled to solve only one question at a time. To Find: i. limy→01+xsin1x1+xcos1xii.…

Q: 2) IF f(x) = {" (x + 2 , – 1<x<0 x, 0<x< 1 find limf(x) %3D

A: To find lim(x tends to inf) f(x)

Q: lim In(r) - 0t

A: Consider the given limit

Q: lim - 1, avx + 3 – b x - 1 lim If score А. 4 D. В. 2 С. 1 E. -INI14

A:

Q: 3 k3 -ル+} (my)0, t) 4 +n -y lim

A: Given that  Limit

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

A:

Q: Show that 4z2 z2 +1 1 (b) lim- z→1(z – 1)3 (a) lim : 43B = 00; (c) lim = 00. - - z(I – 2) 0+2 I- 2…

A: We will use the simple calculations using some usual formulae to evaluate these limits.

Q: f (x+h)- f(x) 7x3-2x-1 Using lim-0 Find the slope of the tangent line y 5x+2 h at x = -1.

A:

Q: 1+t-V1-t lim

A: To evaluate: limt→01+t-1-tt   if we substitute t=0, we get 00 (indeterminate form)   Consider…

Q: Find Lim-0.0 (r² + y²) In(x² +y²) '(xy)(0,0)

A:

Q: (t³ + 8)-dt + 8)-šdt lim

A:

Q: Vx- 2 4. lim- x-2 x2 - 4 y-1 5. lim- Vy? +3 – 2

A: We can apply the limit to the expression by applying the limit as value for the variable in the…

Q: - m- J. lim x - 3 * x + 2 lim 2: *2x + 2'x² - x -6 3 m4 as x approaches m lim 2x – 12 lim x-+6 Vx –…

A: According to our guidelines, we can answer only 3 subparts of a question. Others can be reposted.

Q: の3 Find lim メy <xiy)-s(0,01 x+y² along the curve y=x²

A:

Q: 6 lim | 3 x² – 32 X+3 X - Enter I for oo, -I for -00, and DNE if the limit does not exist. Limit =

A: We shall find left hand limit first if it doesn't exist then limit not exist, if exist and finite…

Q: 2n j3 lim - 24n n00 j=1

A:

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

A:

Q: Prove the limit doesn't exist

A: cc

Q: z² +et= 1-400 2z-e² 2* - 3* 17. lim- x-0 18. lim cotxln(x+1) x-0 16. lim-

A: Note: As per our company guidelines we are supposed to answer the first three sub-parts of the…

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

A:

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: z+3 lim- %3D iz Z+2

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

A:

Q: (1) lim,-0 √x+9-3 X (2) lim-0 1–c05x x sinx (3) limx-1 x²+3x-4 x-1

A:

Q: x+y lim In ху (xy)-(1,1)

A:

Q: Q2: (a) By using " L' Hopital rules "; Find the limits of ::- (1) lim,-(n/2)-(tan x)cosx (2) lim,--0…

A: L'Hôpital's rule states that for functions fx and gx which are differentiable on an open interval I…

Q: Along the path a = e" find %3D lim (7,y) (1,0) y²-6ry 3r-y-3 O 2 O -2 O-3 O does not exist 0 3

A: we have to find the following limit

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: x2 dx. Which of the following options is correct? 00 Consider 9+x6 00 Arcsin 9. + lim - Arcsin 3 A…

A:

Q: (r-2)(z²–3z+4) Use the graph of f(x) = (x-2)(z²–3z+4) (포-2) to evaluate lim- (포-2) O 2 3 does not…

A:

Q: 5. Show that lim –nx² e dx = 0.

A:

Q: 3 limy 0 1 - x!

A: This is the problem of limit and calculus.

Q: 4xy lim Compute the (xy) (0,0)

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: (1) lim t2 (2) lim x0 Vx2 +3 2x + 1 -1 x00 7 - t2 x2 1 (4) lim 3t2 n2 (6) lim x0 Vn3 + 2n 5t (3) lim…

A:

Q: 1ogx -[X] where,nÎ Nand[.]denotes the greatestinteger function. [x] Evaluate:lim- x®Y

A:

Q: x-3x+5 by X-0 4x2+2x+3 10. Find the limit: lim means of the L'Hopital Rule

A:

Q: 13x3sin(는)= 13 2.플) .3, lim %3D (x.y) → (1,-

A:

Q: (x +2x =-6x if xS-2 if x>-2 A) Check the continuity of the function s(x) at x = -2 S(x) = ++ B)…

A:

Q: 2xy Show that lim does not (x,y)→(0,0) x² + y² exist.

A: The limit function is limx,y→0,02xyx2+y2

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

A: Topic = Limits

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.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.