t3 – 1 = 3. t-1 t-1 (c) Lim

Q: 2h 4. lim h0 2h S(x) dr

A: Answer and explanation is given below

Q: 42t lim t+0 4 - 1 - 1

A:

Q: Evaluate

A: To evaluate limx→0 e2x-1xSubstituting x=0 , 00 form is obtained Hence , L' Hospital's rule can be…

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: 5X-T 8. lim -y% = - y-n x+5 a) 0 (b) DNE (c) -n (d) None of these

A: Here y is approaching to π .

Q: sin(1 – t) |2 – 2t| (b) [8 marks] lim t+1-

A: this is left hand limit then limit approaches from left side

Q: tm Ym 3 → Determine the behavior of tm and ym as B → ∞. lim tm lim Ym

A: Given equation is, y''+7y'+12y=0, y0=4,y'0=β, where β>0 The characteristics equation of the given…

Q: 4. Suppose an object with initial velocity vo = 0 ft/s and (constant) mass m slugs is accelerated by…

A:

Q: Q4 / Vx+1–1 A ) Find limx→0

A:

Q: X (b) lim 0 DO (c) lim xln 1

A: (b). Given: limx→0+lnxx

Q: Find the limit. 7e - 7 V1 + t - 1 9. lim t t 1 + t

A:

Q: x² + 4 Find Lim x-0 ex + 1' A. 2 B. 00 С. 1 D. 4 Select one: O A O D O B ос

A:

Q: t2+3t+2 2. lim t--1 t2-t-2

A: To find the limit of the given function

Q: e2t - e-2 – 4t lim- t- sint

A:

Q: x3y along the path y =2x2. Find lim (x.y)- (0,0) x+y2

A: The limit is, 2/5  The detailed solution is as follows below:

Q:

A:

Q: e7x + e-7x _ 2 lim x → 0 5 x2

A: Evaluate the given limit as follows. limx→0e7x+e-7x-25x2=e70+e-70-2502=1+1-20=00 Since 00 is an…

Q: x² + 2ix + 3 lim 1² +1 lim ol z) do not e

A: Using L'Hôpital's rule,

Q: x--2xy lim (x,y) - (2,1) x²-4y² .A 3 .B 1 4 .C .D 1 2 ONIM

A:

Q: 5t2+t sin t 5. Find lim t→∞ t2

A:

Q: E A) Find the value of (H) if, / A: |H 1 -1 (x3-1) 1 = lim,- 0. (x-1) 4 2 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: + h 4 (a) Lim×-1'x+1 X (b) Lim h→0 V5h + 4 – 2 -2 - t3 – 1 3. (c) Lim t-1 t-1 II

A: To show the given limits, we use the algebraic indentity and rationalization of a fraction.

Q: He sold his stock when t = 4. Compute the following (if it does not exist write DNE): Lim-4- J(t) =|…

A: Given,

Q: x²+x y-2y lim (x,y)→(4,16) x- Jy

A:

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

A:

Q: 2-у 4. lim y-4 y2-8y+16

A: 4. limx->42-xx2-8x+16

Q: Along the path x = e find lim (2,y)→(1,0) y²+6zy 3x-y-3

A: To evaluate the given limit: lim(x,y)→(1,0)y2+6xy3x-y-3 along the path x=ey. Here,…

Q: (H.W) sin(t +4t+3) (7) Lim t -9 (H.W) t-3

A:

Q: Along the path x = e' find y²+6xy lim (x,y)→(1,0) 3x-y-3

A:

Q: 2 points f(4+h)-f(4) If f(x) = ax + 8Vx and limh-0 = 5, %3D 3h then a= 13 O 17 O 12

A:

Q: 3x-7 lim zー8 Sx +1

A: limx→∞3x-75x+1

Q: -4x + 2 if r 2 Let f(r) = %3D -5x +4 if r > 2 Find lim f(x), if it exists. z+2 O DNE O-12 -6 0.

A: Given, fx=-4x+2 if x≤2-5x+4if x>2 We have to find limx→2fx if it exists.

Q: nd the one-sided DNE lim_(x². +x+5) x--5- exists). (If an answer does not exist, enter DNE. Submit…

A: Topic:- limits

Q: e-1 t+1 Vi' i +21 ' -1/ In (1 +1)* lim Evaluate

A: Distribute the limit.

Q: 1(a)Find y' given that y In(2x + 1) + e**+5 %3D 5x2-1 b) Evaluate lim x00 2x2+1 c) Find y' if x'+ y…

A:

Q: tan (xy) lim ? (х, у) ->(1,0) у + 2хy (a) 0 (d) - (b) (e) 1 - |3

A:

Q: x*-16y* lim (x.y)¬(2,1) x2–4y2 A 0 B 00 C Does not exist D None of these

A: Topic - limit

Q: t+3t-10 lim t--5 sin(t+5)

A:

Q: t x sin(t + 1) lim --1 t +1

A: Given : limt→-1t×sint+1t+1

Q: 4 6.xy1 Find lim if it exists. (x,y)→(0,0) x² + y8 *

A:

Q: 'e in + = "T 2n Find lim a

A:

Q: 22) Find lim -5 e-2x+6 .given e =2.7 and e0 = 1. = %3D X 3 A) -13. 5 В) - 2.7 C) 0. 0 D) -5.0

A:

Q: x2 – 1 t(2) = 1 What is lim t(x)?

A:

Q: dx X XP (x - 1)ule a-1 lim

A: Given limit lima→1∫0aln1-xxdx. The objective is to evaluate the limit.

Q: Vx+h-Vh 6. lim HW

A:

Q: Inx 1 13. lim, X,

A:

Q: 4f(x) + 2x – 14 Suppose that lim z+1 5. Find lim f(x). I→1

A:

Q: t² +3t t--3t²-t-12 b. lim (-3)²-9 u-0 น (x+h)³-x³ C. lim h→0 h a. lim

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

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.