EXERCISE 4. Evaluate the following using Rationalization Method. Show your solution. Vx² + 7 – 3 lim 1. x-3 x + 3 Vx +1 – 1 lim 2.

Q: ivative of p = 2xz nes maximum in t 3k

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Q: 1 avig srls ni, lim x→-125 x3-5X3+25 ant X3+3 1

A: The limit of a function (expression ) is a value of that function (expression ) approaches as the…

Q: 1. Compute lim. ( ). 1 x→2+ 2 x² – 2x. where c is a real number. You may need to discuss according…

A: limx→2+1x−2−cx2−2x

Q: 2. Select the best answer below: lim (2x-13 X (-1)* O -2 O does not exist

A: We have to find the limit and select correct option

Q: Find the limit. 2 – 4x². - 9x + 11 lim - 8x + 6x +2 X00 11 OA. 2 ОВ. оо OC. O D. 1 F/N 8

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Q: E valuate Dle followneg: lim メーフ+ 7x" – 4x? + 7x - 2 J +- 3 メ 3x° -8x"+ フメー458 -x一5 x3

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Q: b* – 1 Show numerically that for b =3 and b = 5, lim appears to equal In 3 and In 5, respectively.

A: Here given

Q: Describe the left end-behavior off (x) = x´+4x+ 1 o im *+4x+ 1 = -00 lim x²+4x+ 1 x²+4x+ 1 o lim = 0…

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Q: Use the graph to solve for z.* := lim f(r) 3 3 f(x) 2. 2.

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Q: Q. 1. Evaluate the following -x* +3x +5x –18 a) lim 5x – 2x-0.5 Vx² +15 –4 b) lim x-1

A: We have to calculate the limit

Q: For all x ≥ 0, 4x − 9 ≤ f(x) ≤ x 2 − 4x + 7. Find limx→4 f(x). ⇒

A:

Q: 4-The rational function y=ax?/(bx2+(2b+1)x +b) has one vertical asymptote and passes through point…

A: Solution

Q: V5x+9-3 -lim x+0

A: To evaluate: limx→05x+9-3x which is in 00 form. So, the L'Hopital rule is to apply.

Q: Q3: A. Evaluate the limits of two of the following: V2x(x-1) 4x-x 1. limx4 2-Vx Vx2 +8-3 2-V 3.…

A: Given:(1) limx→4 4x-x22-xsolution:limx→4 4x-x22-x=limx→4 x(4-x)2-x                   =limx→4…

Q: find the limit of rational function (a) as x→0 and (b) as x→ -0. x³ + 7x? – 2 g(x) x² – x + 1

A: Given  g(x)=x3+7x2-2x2-x+1

Q: x* – 2x²y + 4y² c) lim x' + 4y² (xyH0,0)

A:

Q: find the limit of rational function (a) as x→00 and (b) as x→ -o. 3x7 + 5x? – 1 f(x) 6x3 7x + 3 -

A: (a) Given f(x)=3x7+5x2-16x3-7x+3 For x→∞…

Q: find the limit of rational function (a) as x→0 and (b) as x→ -o. 5x8 – 2x3 + 9 h(x) 3 + x – 4x5

A: [a]limx→∞5x8−2x3+9−4x5+x+3 Therefore, limx→∞5x8−2x3+9−4x5+x+3=∞

Q: 5* – 1 (a) lim vour cale x + 3 (c) lim 1+0 x2 + 5x + 7

A:

Q: 4. Find the following algebraically. -2x – 4x +4 a. lim x³ – 27 x - 2 b. lim V9x² +1

A: SOLUTION-

Q: Evaluate the limits. t2 – 4 lim 42 t3 – 8 | (a) (b) (9 + x)-1 – 9-1 lim 8x2 – 9x + 1 lim a00 3x2 +…

A: limt→2t2-4t3-8

Q: EX- Find Lim -im Z-2Z+4 Z-1-13i

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Q: 1. Test z = x + 5xy + 10y? + 8x - 40y for maxima and minima.

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Q: 1. For what value (s) of x is the function f(x) = 4/2x2 - 6x not continous?

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Q: Find the limits 2.1 2x + 3 lim Xo Sx + 7

A: To evaluate the limit: limx→∞2x+35x+7 Solution: limx→∞2x+35x+7 On simplifying further we get:…

Q: Find limits: 2x2 — х — 1 lim b) х--1 4 — 3x? - х х* + 3x + 1 lim x+-1 2x2 – 3x – 5 Зх — а) V- 2 lim…

A:

Q: 1. Find the limits: [Vx² – 5x – x + In („)) 2x²+4x 7x³+2x²+4x+9° b) lim X-1 5x²+13x+8

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Q: Find the limit 4x2+17x lim x+0 ex-1 a. 1 17 b. None of these. c. с. О O d. 17 е. 1

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Q: 18) Find lim f(x) %3D X 2 - A) – B) 2 00 C) 1 D) 4

A: Topic = Limits 18) B

Q: Q2. Evaluate the following 4-x2 1. lim x→2 3-Vx²+5 t²+3t+2 2. lim t--1 t2-t-2

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Q: lim 2. e

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Q: Find the limits t +3 a) lim (4x3 – 3x² + x – 85); b) lim, t+2 t+1 ; c) lim x +0 1-V1+7x ; d) lim (7…

A: We can solve these problems in this way

Q: Show that 13x - 12 can be made as small as desired by taking x close to 4. lim(4x 2 + 2x + 5) = 5x➔0

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Q: Consider the function f(x)=xe^-7x, 0≤x≤2. Find The absoulute mininum and maximum.

A: Given data: The given function is f(x)=xe-7x. The given limits of x are [a, b]=[0, 2]. The first…

Q: Find the vertical and horizontal asymptote(s) of f(x).

A: Vertical asymptotes are vertical lines which correspond to the zeroes of the denominator of a…

Q: 3. Find the following limits: x2 +5x +6 (a) lim x-3 x2 + 4x + 3 Vx2 + 5x +7 (b) lim 5 – 2x (c) lim…

A: As per our guidelines, we can not solve  more than 3 subparts so please repost  the remaining  part…

Q: Use the Intermediate Value Theorem to prove that 8sinx = x has a solution between and a. 2

A: Let us consider a function f(x)= 8sinx-x

Q: ラメー 2. for) = X ニ 3メ-1 lim (fog)x メーラ

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Q: V1+3x-1 lim Answer: 1 %3D

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Q: Evalnate the fo llowing limits 1. lim 4x-5x+1 メ→ -4x? 2. lim I x²+5x -6 X- 4 lim (1x-7)* 3. 2.

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Q: If f(x) = 4" , then lim %3D (A) 4 (B) ! 1.

A: f(x)=4xlimx→0f(x)-f(0)x-0=limx→04x-40x=00, indeterminate form. Apply l'hospital rule to simplify

Q: If p(x)=x²+2x -3 and q(x)=x3-1, then lim 3p(x) 4q(x) x+1 II

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Q: Which of the following is your solution to lim Vx² +2 = ? x-0 3x -6 O 1/3 O -3 O -1/3 O 3

A: Given  The limit expression is  limx→∞x2+23x-6 .

Q: Vx+12-4 3. Confirm your result in the problem 2 by evaluating lim x→4 algebraically. x-4

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Q: 16) what are the vertical asymptote(s) of f(x) = x+5x-6, %3D x² -1

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Q: lim 3x²-5x+6 x2+x-3 lim (s+t)?-t2 S-0

A:

Q: 1. If the rational function y = r(x) has the vertical asymptote %3D x = 2, then as xr→2*, either…

A: Given: y=rx

Q: The value of the constant k such that x2-kx+7 lim exits is x-1 x+1 -7 7 -8 8 -6

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Q: lim ( 7x 12 6. lim 13B

A: In this question we can find limit . Firstly solve quadratic equation of the numerator and cancel…

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.