ure E-S theorem to prove the following lim (9x+5) = - 32. x→3

Q: 5. Evaluate lim sin(x)-(x² +3x– e*). 1-0

A:

Q: et +e-& – 2 Evaluate L = lim Hint: use L'Hospital's Rule. 1- cos x |

A: Use L hospital rule

Q: lim (In(x))½ ?

A:

Q: 5 tan(4x) x→0 3 sin(2x) Evaluate lim using L’Hôpital's rule.

A: The  L'Hopital's rule is: Suppose, f(x) and g(x) are two functions and their limit is given as:…

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

A:

Q: A tank initially contains 50 lb of salt dissolved in 250 gal of water. Starting at time t = 0, water…

A: A tank initially contains 50 lb of salt dissolved in 250 gal of water. Starting at time t = 0, water…

Q: 1S 章テ(メ) H+3x寸hen lim トーつ0

A: the objective is to find the derivative of the given function by using definition of derivative

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: Find lim "(x.y)→(0,0) (4 + (x² + y? ) In(x² + y² )) Dose not exist O 1 4

A:

Q: lim In(r) - 0t

A: Consider the given limit

Q: et+ e-X-x2-2 d. lim- x→0 sin²x-x

A: Since there is the symbol of limit, hence limit of the function helps to find the answer to the…

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

A:

Q: 2x 14x + 20X Limits. Evalute lim X-5 rounded to 4 decimal places x2 - 6x + 5 O 0.1333 O 1 O 0.5 O 2…

A: We can find the limit as below.

Q: Find lim (2+x)" * using L'Hôpital's rule. 1/x

A: Given the given expression is limx→∞2+x1x.

Q: Let Fexy=4 Find Lim FAt and Lim FEX) X->2* 2 Does l tM fe) exist? Why zis FM cON tin-noss at X=27…

A: Answer

Q: lim,-o ([sin x]*) is

A:

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

A:

Q: lim In(x2 + y?) (x,y)-(0,0)

A:

Q: Q2/Find the limiting values: lim Tan (4%) 必→。 O lim 7 7- x2

A: Explanation of the solution is given below...

Q: 1. Find the limī lim In(sin x) X→π-

A:

Q: d. lim h(x) Preview e. lim h(x) = x→00 Preview f. lim h(x) = 00--x

A:

Q: Let ƒ(x) = (x2 - 1)/( | x| - 1). Make tables of the values of ƒ at values of x that approach c = -1…

A: Make tables of the values of ƒ at values of x .

Q: Along the path x = e find lim (1,y)→(1,0) y2-6ry 3x-y-3 O 2 O does not exist O -3 O 3

A:

Q: Evaluate limx=0+ e(1/x)

A:

Q: lim 4y° + Jy18 – 1 -00

A: Given that: limy→-∞4y9+y18-1

Q: 1 4. Find limx→0+ ( ) ex-1

A: Given :          limx→0+1ex-1-1x

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

A:

Q: 2017 3 Example 9 Prove that lim vx +x² sin = 0.

A: Solution: The objective is to prove the given limit value is 0

Q: Hws] lim x = 5 E 5e •Prove

A: Given sequence xj=5j-1j+2j∈N we have to find limj→∞xj limj→∞5j-1j+2=limj→∞j5-1jj1+2j       (Taking j…

Q: (c) lim 1 In x x→0+

A: To find out the limit

Q: Find lim (e-2x cos x) (Hint: Squeeze Theor

A:

Q: Along the path x = e" %3D find y +4xy lim (x,y)-(1,0) 3x – y - 3 does not exist O -2 -3 2 0 3

A:

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: 2. (a) lim T-cos e (b) lim. -70 In R tim (0) メーール

A:

Q: 15. Investigate In (x + 1) In (x + 999) lim lim and In x In x Then use l'Hôpital’s Rule to explain…

A: L' Hopital's Rule is used in the following cases,

Q: - Find the Lim;t: O Lim Sinx メー0 12ナメ3 E. 4) Lm sint2 sino lim 下-日

A:

Q: Given n ≥ 0;  explain that   limx→∞ fn(x)/(e^x) = 0.

A:

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: Could you use L'Hopital's rule to solve the following question in its current form: lim,0+ In(x+1) O…

A: We have one of the following form limx→af(x)g(x)=00 or  limx→af(x)g(x)=±∞±∞  In these cases we have…

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

A:

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

A:

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

A: Topic = Limits

Q: Find the limit. (Round your answer to four decimal places.) lim In(x - 8)

A: We will find this limit algebraically  We pick a few x values which are close to 8 from the right…

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: Which of the following will make limx→c f(x) and f(c) equal? limx→2 : (x²+x-6) limx→–1 (x³ − 2x + 3)…

A:

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.