1. Rules of LDef nite Integrals: 12 a) b) rpx 12 12 f(x)dr 4, find the If f(z)dr = 12, " $(z)dz = 6 and " following: %3D 12 |

Q: Fnd the average value of the function over the glven Interval. (Round your answer to three dedmal…

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Q: Problem 3: Given a function 4 - x2 g(x) = 3 - Vx2 + 5 Page 1 of 3 Use analytical method to determine…

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Q: Q2: Solve the following integrals:- (2) fd 4x2-9 xp: (3)fx sin(x +1)dx

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Q: 6. Let 4-x? < f(x)< 4 + x². Use the sandwich theorem to determine the limf(x). Show all work!

A: Use sandwich theorem

Q: D. Find the orthogonal trajectory f the family of curves y= x+h %3D

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Q: Find div F and curl F if F(x, y, z) = 16y°z³i – 9x°z°j – 7xy'k. - - div F= curl F=

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Q: The graph of y= f (x) is drawn below, sketch a graph of y = f(x).

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Q: 5. What is the general solution of the following differential equation ( .6³yod?y =0)? ,d*y +9. dx2…

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Q: 7. Į V1- xdx 8. ſ e2x dx

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Q: An advertising agency spends £x on a newspaper campaign and a further £y promoting its client's…

A: The Multiplier Method of Lagrange We may need to maximize (minimize) a function that is constrained…

Q: dy when x = 1 is dx If y = e-ª In x then A) 0 B) Does not exist D) = E) e

A: We have to find the dy/dx    at x  =1

Q: Suppose a certain baseball diamond is a square 90 feet on a side. The pitching rubber is located…

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Q: If y = x2 is expressed with parametric equations such that = 6 when x = 1, what is ? dt dx %3D dt

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Q: Answer the question in FULL details. Show ALL your steps and work in your calculations. Answer in…

A: We want to find the absolute extremum of the given function on the interval [-2,2]

Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of • sin ( z) h(x) = |.…

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Q: Consider the following. 3x - y + z = 6 Sketch a graph of the plane.. y -6 y -4 2 y 4. 2 2. Label any…

A: Given :3x-y+z=6To find it's intercept

Q: True or False: If lim f(x) = 2 and lim g(x) = 4, then lim[-3f(x)² – 49(x)] = -4 %3| True O False

A: Given: limx→afx=2 and  limx→agx=4.

Q: S2 2 sin?x cos5x dx =?

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Q: Evaluate the definite integral (12a² – 6x + 6)dx 3.

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Q: 2. A rocket is launched in the air. Its height (in meters above sea level) as a function of time t…

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Q: Answer the question in FULL details. Show ALL your steps and work in your calculations. Answer in…

A: We need to solve differentiation problem.

Q: Evaluate the definite integral 6 sin(x)dx

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Q: Find two positive numbers that satisfy the glven requirements. The second number Is the redlprocal…

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Q: valuate the integral by interpreting it in terms of areas. In other words, draw a picture of the…

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Q: 4. S(9x + 33x +22) dx

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 4 of 21 Which of the following is not an identity? I. tan z + cot z = sec z csc z II. cos? z = sin…

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Q: 5sin e Cose de Sin? o +3 Sine -4 2.

A: Solve the following

Q: Speedometer readings for a vehicle (in motion) at 11-second intervals are given in the table. t…

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Q: Find all points (if any) of vertical tangency for the curve represented by x = t? + 2t – 3 and y =…

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Q: * Find the 2nd degree Taylor polynomial for the function f (x)=- 1 centered at x = -2.

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Q: For x = t3 + 2, y = 3 – t, give an equation in terms of x and y.

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Q: 2x2 -9x Find the limits and justify if needed. 12. lim x² – 1 X-

A: Given query is to find the limit of the expression.

Q: sin(n +h) – sin . lim- а. 1 b. 0 C. -1 d. * е. -00 h-0 h

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Q: Find the volume of the solid obtained by rotating the region bounded by the given curves about the…

A: Given:-the region bounded by x=y4,  x=1rotating about the line x=7using washer/disk…

Q: J4-yズ ニo dy

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Q: Find 8 i8 Z = -12 ti2

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Q: How do you solve related rate problems in calculus? List all steps.

A: Step to solve rate related problems in calculus

Q: 5. Find the Maclaurin series for f(x) = In(1 Do not use the building block from the previous…

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Q: Evaluate the definite Integral by the limit definition. (x2 + 4) dx

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Q: Find both first partial derivatives. Z = cos(4xy) %3D Oz %3D ду

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Q: An object weighing 1000 pounds sinks in water starting from rest. Two forces act on it, a buoyant…

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Q: Find the Taylor series generated by f at x = a. 1 f (x) a =3 4-x

A: Solve the following

Q: Use Disk Method only Find the volumes of the solids generated by revolving the regions bounded by…

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Q: I. Complex Numbers and Variables 1. Find the square roots of the complex number 5 + 2i. (cos 0+j sin…

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Q: Which substitution is needed to evaluate the integral S tan* x sec² x dx =? u = tan* x, du = sec? x…

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Q: Problem 3: Given a function 4 - x2 g(x) = 3 - Vx2 + 5 Page 1 of 3 Use analytical method to determine…

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Q: What is an equation for the cosine graph shown below? 11 -10 -8/ -6 -5 .4 -3 -2 -1 -135 -90 -45 45…

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Q: (d) sec(x) – sec(x) sin²(x) = cos (x)

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Q: Use Lagrange Multipliers to solve the following: Maximize f(x, y, z) = 4.x + 2y + z subject to æ + y…

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Q: Consider the function f(t) = 6 sec (t) – 6t°. Let F(t) be the antiderivative of f(t) with F(0) = 0.…

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