1. Prove the following limit. a) f(x)=x²+2x+6 where lim, 3 f (x)=21 x→3 b) limx? -x+1=-5 c) lim x→2 x² =8

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Q: Evaluate the definite integral. 1 5x +6dx

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Q: (1 – x²)dx eTextbook and Media 2) V You answered correctly! Move on to the next part to add to…

A: According to guidelines we solve only first question.

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A: we know that,           integration of xn dx = xn+1n+1.  and x-y2= x2+y2-2xy

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Q: Suppose that f(x) is a differentiable function satisfying the table below. 0 2 f(x) | 1| 2 | 12 | 7…

A: The objective of the question is showing that there exist at least one x=c for which f'(c)=5.

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Q: 5. Use differentials to app. .. the value of V(3.01)² + 2(0.99) – 3 in four decimal places. o 5.…

A: I am attaching image so that you understand each and every step. Let x= length of box y=width of box…

Q: usider (x. Using a suitable trigonometric substitution, the resulting integral in terms of 0 is…

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Q: cos (x) tan (x) dæ

A: I have stated the used formulas in the solution

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Q: Complete the following KenKen puzzle to determine what is represented by x and y?

A: The rules of KenKen puzzle is: Use each number only once per row, once per column. Cages with just…

Q: " + Oy' + 9y = 0, v(0)= 1 and y'(0) = 4.

A: The given IVP is y"+6y'+9y=0,   y(0) =1, y'(0)=4 we have to solve the IVP.

Q: to the South Coast Air Quality Management District, the level of nitrogen dioxide, a brown gas that…

A: Here,  A(t)=0.03t3(t-7)4+60.2, 0≤t≤7

Q: Given: dx x3 Using trigonometric substitution, solve for the integral form in terms of 0.

A: This question can be solved by taking x=3secθ

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Q: Find the velocity and acceleration vectors in terms of u, and ue. d0 T= a sin 60 and = 5t, where a…

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Q: s-8 3. (s-3)(s²+2s+17)

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Q: 2.S Ver eax dx Sve

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Q: Let C be a curve that is defined by x = 4 sin t and y = cos t, t e [0, 27). Determine (a) the time…

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Q: Find an equation of the tangent plane to the given parametric surface at the specified point. r(u,…

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Q: S x2 +2x-10 (2x+4) + 1 JE + 4x +5) Consider dx = x² (x² + 4x + 5) (2x+4) + 1 dx- x² + 4x +5 dx ,…

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Q: 5x dx? x3 + x2 +4x+4 How many quadratic and distinct factors are in the denominator of

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Q: Given: dx x3 Using trigonometric substitution , solve for the integral form in terms of 0. A sin? 0…

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Q: y" + 4y' = cos(t – 3) + 4t, y(3) = 0, y'(3) = 7

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Q: 3r + cos z Use Squeeze Theorem to evaluate lim VI+x² – 5x°

A: Given problem:-

Q: r³ – 4x – 1 = 0 3 | Consider the implicit curve throughout this problem. Find dy/dx and use this to…

A: We can solve as follows

Q: x³ + 6x² + x +2 dx? How many quadratic and distinct factors are in the denominator of x³ +1

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Q: 6. A bax with a square base is to have an open top. If the lateral surface of the bax is 100 cm",…

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Q: Find the curvature and the radius of curvature at the stated point. r(t) = 11 cos(t)i + 10 sin(t)j +…

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Q: Consider the following function. f(x) = x3 – 3x2 - 9x + 5 Find the first and second derivatives.…

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Q: g(b) Use the Substitution Formula, f(g(x)) g'(x) dx = | f(u) du where g(x) =u, to evaluate the…

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Q: 1/2 x2 The result of dx is F(b) – F(a); where F(a) and F(b) are real numbers. What is the value of F…

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Q: Let C be a curve that is defined by x = 4 sin t and y = cos t, t E 0, 27]. Determine (a) the time…

A: Let C be a curve that is defined by x=4sint and y=cost, t∈0,2π. x=4sint⇒dxdt=ddt4sint=4cost…

Q: Find the point on the line y = 5x + 2 that is closest to the origin. (x, y) = Need Help? Read It…

A: Let's find.

Q: Evaluate the definite integral. O el4 – 1 i+ (e- – 1) j+; 14 O el4 1 i- ej+ k 14 2 (e4 – 1) i – (e-…

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Q: I. Evaluate 4x² + 4x + 5 dx

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Q: Assuming that z is a function of x and y, find the equation of the tangent plane and the equations…

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Q: Given the equation below, find dy/dx* 6x^3+2x^30 y+y^4= 9 dy/dx= Now, find the equation of the…

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Q: Question- Let R be the region bounded by y= x+2, y30, and x=3. Then draw the region and evaluate the…

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Q: If 7-4/3 = Vx-Vy, determine the values of x and y. %3D

A: We have to find the values of x and y from the above expression.

Q: S csc6 cot* w dw W

A: Given,           ∫csc614wcot414wdw

Q: 4. x2(y + 1)dx + y² (x – 1)dy = 0

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