I. Evaluate the following integrals. 3.x5 dx V2 – x3 1. - 2* + e2" sin(2") dx sin(2") 2. 2x + 3 dx 4x + 5 3. 4x2 -

Q: Let p(x) be a polynomial of degree 3. Its derivatives, around the point æ = -5, are as follows:…

A: solution:-let p(x) be a polynomial of degree 3p(x)=ax3+bx2+cx+dwhere a,b,c & d are parametersat…

Q: Jse the linear approximation to estimate AS = f(3.1) – f(3) for f(x) = T Use decimal notation. Give…

A: Here, the given function is: f(x)=31+x2⇒f'(x)=3-1(1+x2)2(2x)=-6x(1+x2)2

Q: 3 c2x S *x² dy dx 4.

A: Integral

Q: A manufacturer has an order for 1000 units of fine paper that can be produced at two locations. Let…

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Q: A right circular closed cylinder with radius r cm and height h cm is placed on a square block with…

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Q: 2. All edges of a cube are expanding at a rate of 6 centimeters per second. How fast is the surface…

A: We have to find changing the surface area

Q: Acos'e -3=-4cos0

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Q: SíS(x² + y²) dx dy 0.

A: To evaluate the given iterated integral.

Q: Evaluate the integral by any method. NOTE: Enter the exact answer. dx 3+ x4 %3D

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Q: Consider the following. f(x) = x3 – 12x

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Q: x = -2t Given: line l1 : 3 1 – y = Z - 8 and l2 y = 2 + 2t z = 6 + 2t %3D 1. If the given lines…

A: The solution is given in the next step.

Q: S Зх-7 dx 10х2+3x+11

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Q: Find the net signed area between the graph of the function f(x) = |x +3| – 4 and the r-axis over the…

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Q: A plane P, in R'is perpendicular to the vector i = (4, 5, 7), and contains the point (3, 3, 8). a.…

A: A plane P1 in R3 is perpendicular to the vector n→=4,  5, 7, and contains the point 3, 3,  8.a To…

Q: . L'Hôpitaľ's Rule Evaluate the following limits or explain why they don't exist. 1 lim 1 X→0 sin x

A: Rewrite

Q: Prove the following identity: 1- tan? e cos 20 = sec e

A: solution:-cos2θ=1-tan2θsec2θ RHS=1-tan2θsec2θ        =1-sinθcosθ21cosθ2,      ∴tanθ=sinθcosθ &…

Q: A deli sells 720 sandwiches per day at a price of $6 each. ... A market survey shows that for every…

A: Let price reduce x times Price of deli = 6 - 0.1x Number of deli sells = 720 + 20x   Revenue

Q: 6. S 2sin´x sin(2x) dx

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Q: Graph y = - cos (x -) by Transformation of y = cosx. Show and label each Trigonometric function…

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Q: S 3p? tan" p dp

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Q: S sin? 3c cos? 6c dc

A: Solve the following

Q: Зх-7 dx 10x2+3x+11

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Q: Use Shell Method only Find the volume of the solid obtained by rotating about the x- axis of the…

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Q: 4-P(1+) che model A=Pe or A=P|1+- ] ,where A is the future value of P dollars invested at nuously or…

A: we have to find the interest rate

Q: Find the Taylor series generated by f at x=a. f(x) = 1/x2, a= 10

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Q: b.

A: answer is in next step

Q: Find the arc length when y = 2 ln(sin ) and /3 << x < T. %3D

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Q: Find the area A of the sector shown in each figure. (a) 72° 4 A = (b) 0.5 rad 16 A=

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Q: Current Attempt in Progress Evaluate the definite integral two ways: first by a u-substitution in…

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Q: 3e" da V4-e2a

A: We have to find out the integral

Q: Find p1 and p2, the prices per unit (in dollars), so as to maximize the total revenue R = X1P1 +…

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Q: Question 3 (a) Find the first and second derivative of the following function, in which a and b are…

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Q: olve the equation. Write the solution set with the exact values given in terms of common or natur…

A: Given query is to find the value of y.

Q: x=t² +3t +5 Determine the arc – length of the curve: y = (2t- +2

A: solution:-given curve x=t2+3t+5y=232t+43/2+2dxdt=2t+3dydt=22t+4

Q: In each part, evaluate the integral, given that SIx - 61, x 2 0 f(x) : x + 6, x < 0 ' %3D

A: The solution is given in the next steps.

Q: Find the slope of the tangent line to the r=2-3cos 0 in polar coordinate at 0 =

A: Given:-r=2-3cosθdrdθ=3sinθTo convert from Polar Coordinates (r,θ) to Cartesian Coordinates (x,y)…

Q: Sólvé thé équátión ón the interval U30<2T. 0<2x. 4 sin 0 + 5 = 7

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Q: Suppose that P dollars in principal is invested for t years at the given interest rates with…

A: Solved below.

Q: Evaluate the integral using the appropriate substitution. You must use a substitution for this…

A: Given query is to find the integral.

Q: y 5| 3 2 -4 -2 -1F 4. 2.

A: We find the point where limit does not exist

Q: 3 Use the linear approximation to estimate Af = f(3.1) – f(3) for f(x) = I+x (Use decimal notation.…

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Q: The focus of the parabola defined by the equation x2 = 20 y is (4, 5) (0, 0) Option 1 Option 2 (0,…

A: Given query is to find the focus of the parabola.

Q: dr 21. (1+x²)/16 – (tan-l r)² dx e2x+2+2 22. 8. dx x2 - 6x + 25 23. 6. 24. dr J (2 - r)V - 4x +3 dr…

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Q: 3s 14 82-4s +8 - 3e cos 2t + 4e2" sin2t 3et cos 2t –4e2" sin2t - Option 1 O Option 2 4e2t cos 2t +…

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Q: Integrate sze" • fa". de Answer:

A: We have to find the integral

Q: 3) lim-) 1 х-1 \x-1 In x)

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Q: Let F(x) = (f(x))² + (f'(x))², F(0) = 6, where f(x) is a thrice differentiable function such that…

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Q: A right circular cone has a base radius of 6 feet and slant height of 10 feet. If the approximate…

A: We can solve the given problem by using differentials.

Q: dx Vx-4x-7 S- -dy y2-8y+5

A: The given integrals are' 1)1/sqrt(x2-4x-7)  2)7/(y2-8y+5).

Q: Write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as…

A: We have to simplify