V3.x – 3 Зх — lim I-3 r # 3 х — 3

Q: Q1/ A) if a = 2i +4j b = 3i - 2j + 4k C = 4i + 2j - k d = 3i - 5j + 4k Calculate ( b x c). (d – a).…

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Q: ebraically. f(7 + h) – f(7) lim where f(x) = -x² + x + 6 h-0 h E Keypa Keyboard Shortc

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Q: Find the exact value of x. 45° 100 Lim (O [0] 7h 15 VI UC

A: The sine of an angle is the length of the side opposite the angle divided by the length of the…

Q: If a ball is thrown into the air with a velocity of 40 feet per second, its height (in feet) after t…

A: The height function of the ball is given by yt = 40t-16t2 To evaluate: An expression for the…

Q: Q1/ Find the following 1. lim + 2 = 3 X00 X 2. lim(5x - 4 + )

A: according to our guidelines we can answer only three subparts, or question and rest can be reposted.…

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: Find the length y=(x+2)^3/2 for x in the range 0≤x≤2.

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Q: IF FLX)= and Lim F(X)6 F(-)=2 b X<l Find a,b when X#0

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Q: Which of the following corresponds to the x-4 √x-2 evaluated? 0 4 2 DNE limx→4 ( when

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Q: Approximate the value of 2x + x lim e" – 1 by substituting in 3 different values of x that get…

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

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Q: Among the solutions of the 3rd order linear ODE y" – y" + y' – y = 8et, only one function satisfies…

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Q: V10x – 7y – 10 Find lim by rewriting the fraction first. 10x - 7y – 100 (x,y)→(10,0) 10x - 7y + 100

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Q: If lim,--2+95; (z + 4z) = x + iy, what is the value of x - y?

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Q: If V5 – 2x? < f(x) < V5 – x? for -1 <x < 1, find lim,-o f(x).

A: Given  5-2x2 ≤ f(x) ≤ 5-x2 for  -1≤x≤1.

Q: (x+h)³-x³ h C. lim- h-0

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

A: SOLUTION-

Q: Q. 2 Find the following limits v' -8 a) lim v* –16 v+ 2 4x –x 2- Vx b) lim 4

A: The limit of a function is the value of the function at which the arguement for the function tends…

Q: Write ∞ or -∞ where appropriate.

A: Given  limx→∞1x1/3-1x-14/3

Q: lim Sin (X+lTly)! X-T/4

A: If limit is not an any indeterminate form then put the values directly.

Q: ах? + bху + су? y-0 dx + exy + fyx“ ax? + bxy + cy 2. Evaluate lim lim- – lim lim y-0 x0 dx +exy +…

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Q: Among the solutions of the 3rd order linear ODE y"-y"+y'-y = 8et, only one function satisfies lim y…

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Q: H.w iF FX)= *+b x<I and Lim F(X) 8,F(-1)=2 Find asb and when X#0

A: Solution:

Q: Find lim v² + 2x – x. (а) 0 (b) 1 (c) 2 (d) o (e) DNE

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Q: x²+x y-2y lim (x,y)→(4,16) x- Jy

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Q: For f(x) = the square root of 7x+30, how can I find f’(x) using the definition f’(x) = lim as h—>0…

A: Given,          The function is fx=7x+30.We know that,          The derivative of the function is fx…

Q: Find the Limit 2 - V? 3b. lim 1-2 r + 2 - Va? + 4x + 4

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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: Please find the limit (in terms of the constant a).

A: it is given that

Q: If lim,→-8+11i (z² + 16z) = x + iy, what is the value of x – Y?

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Q: k lim (1+†) k→∞ k

A: We have to find limit

Q: al Find lim txy (,0) f Excts Find lim 4xy (0)

A: a We have to find the limx,y→0,04xy2x2+y2 if exist. Take any path y=mx Then…

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: 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: Find the following (x – 4)5 lim 1-4 (r – 4)3 1² – 16 lim t² – 4 lim t2 t3 + 8 (a) (b) (c) I→-4 I +4

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Q: Using the Sandwich Theorem

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

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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…

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Q: 1) Answer the following: 1. Find: lim-5-25 x-5 2. Find x2 + y? = 9xy dx 3. Find y': y = 5 sin3x

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Q: (c) lim r³/x² 3/22

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

Q: Find the values of the constants a and b such that

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Q: n+h 1 - Determine lim h→0 h V1+ sint dt and justify your answer.

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Q: 52² – 5y? lim (2.)(0,0) 7x2 + 7y

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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: x? - 2xy +5y lim (a. yl-10.0) 3x2 + 4y² 4x'y lim x' + y (X, -(0.0) lim (x. y-10.0) +

A: We will answer the first three questions as you didn't mention any. Please resubmit the other…

Q: g lim y²+6y y¬T [/y+1-3y2 y+1-3y²

A: Using standard limit substitution

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: Find the value of lim f(x), if f(x): I6+ S8x +5 6 %3D O 52 О 16 O 20 О 32 O 10

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Q: The lim as we approach the point (0, 0) along the path y 3z is: (z,y) (0,0) 12 + y? Select one: None…

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Q: Evaluate in terms of the constant a.

A: We have to evaluate the limit: limh→0a+2h-ah Since it is 00 indeterminate form ( after putting h=0…

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.