1 3. S (х+1)(x2+4)2 dx

Q: In this problem, please evaluate the trig functions without a calculator and do not use a decimal…

A: Equation of a tangent line of y=f(x) at (x1,y1) is given by, y-y1= [dy/dx]at x=x1 (x-x1)

Q: Suppose that f '' is continuous on [1, 3] and f(1) = 3, f(3) = −4, f '(1) = 5, and f '(3) = 4.…

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Q: Determine the value of 3A+1OB if 14x2 + 33x + 9 Cx + B %3D (x – 1)(x+ 1)2 x - 1 (x + 1)2 Answer:

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Q: is xZ dz dx dy

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Q: Find the equation of the tangent line to the curve y 3 sec z 6 cos z at the point The !! equation of…

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Q: The population of a town can be modelled by the exponential equation P(n) = 12000(1.02)"-2015, where…

A: If p(n) is the population of the town then  p'(n) is the growth rate of the population.

Q: Q2) Convert the polar function r tan20 to cartesian. %3D

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Q: 7. S(x – 9)7 dx 8. S: r5 dr V3-r6

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Q: Use the derivative f’(x)=x^2(x-5)(x+5) to determine The local maxima and minimal of f and the…

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Q: 3. The radius of a sphere is increased from 20 cm to 20.2 cm. Estimate the change in volume.

A: First write the volume of a sphere and then diffrenciate it and put all the values.

Q: Find the radius of convergence, R, of the series. (x + 4)" R Find the interval, I, of convergence of…

A: The given series,        ∑n=1∞n6nx+4n

Q: Question 7 Find the area enclosed by the curves y=2r², y=2x.x=- and x = 1 A) 45/51 B 65/89 59/76 D)…

A: Here is the solution

Q: (а) у"— (а + В)y' + аBy %3D 0 (а + B)

A: Answer as follows

Q: is said to be the Laplace transform of f, provided that the integral converges. to find L{f(t)}.…

A: Let's find.

Q: Find the arc length of the polar curve described by: r = 5+ 5 cos 0

A: Use the formula for the arc length in polar coordinate.

Q: Use properties of logarithms with the given approximations to evaluate the expression. log 3x0.477…

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Q: The solution of the initial value problem: 1 dy X +1 dx 1 for which y(1) = 1 is y

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Q: dx 4. S x2Vx2-1 e Cos-1x 5. S 6. Se sin(In x) dx V1-x2

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Q: Determine which expression is the correct rationalization of the numerator of Vx+1-5 x+ 24 x+1 +5 x-…

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Q: Find an equation of the tangent line to the graph of y = x^3 − 1 at the point where x = 2.

A: To find the equation of the tangent line at x=2.

Q: Find the area of the shaded region Blank 1 Note: Enter exact answer x = y 20 1000 y? 20

A: x=yx=1000y2Solve both the equationsy=1000y2y3=1000y=10The limits of y are from 10 to 20.

Q: xsin x dx

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Q: Compute the composite functions fog and gof and discuss their domains, where f (x) =vx, g(x) = 1 –…

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Q: Jackie wants to design a cylinder shaped container to hold popcorn. Each container will be made from…

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Q: Find the smallest value of x for which the series Σ (x+101)" 2ln(n) n=2 is conditionally convergent.

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Q: Use Theorem 7.1.1 to find L{f(t)}. (Write your answer as a function of s.) f(t) = 4t2 – 2 sin(5t)…

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Q: Find all second-order partial derivatives of the function f(x,y) = x + xy – 5x³ + In(x² + 1).

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Q: (x+a)² 3. Let f (x) where a is a constant and a -1. (Note if a = -1, then f(x) is a line %3D x-1…

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Q: 1. a) Find the linear approximation of f(x) = Vx at x= 27 %3D b) Use it to approximate V26.9

A: To find linear approximation of given function

Q: quation and reduction to linear ec

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Q: Problem: At time t = 0 there are 10 person in a community of 1,000 people who has the flu.…

A: Required formula:  Logistic growth model: Nt=K1+K-N0N0e-rt Where,  r = Exponential growth rate…

Q: Evaluate: S(4sin (x) – 3sec? (x)) dx

A: ∫ 4sinx-3sec2xdx=∫ 4sinxdx-∫ 3sec2xdx=-4cosx-3tanxAdd a constant to the solution=-4cosx-3tanx+C

Q: Evaluate the Laplace transform of ecos3tdt. O a. s2+2 s2(s² + 4) Ob. s+ 16 Oc. 2 s(s²+ 16) O d. s?+4…

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Q: Using a method of reduction to separable equation and reduction to linear equation, find the general…

A: Let's find.

Q: Describe the graph of the equation. (8 – 21) i + 13rj r = O It is a plane in 2-space through the…

A: I have appended the formula used in the solution part.

Q: S=sin(In x) dx

A: To evaluate the given integral.

Q: If possible, find AB. (If not possible, enter IMPOSSIBLE.) 0 1 0 B = 3 1 A = -5 5 0 4 2 1 8 6 -1 7…

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Q: Differentiate the following functions: i. v = 15/7(12/7+ 3t) (2x – 9) f(x) = x + 4 ii. iii. y =…

A: We can solve this as follows:

Q: (a) y= (x + 1)? O III OIV (b) y (x- 1)2 01 O II O IV (c) y-x - 1 O II OIV (d)

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Q: Describe the graph of the equation. r = -6i+ (1 – t?)j + t k O It is a parabola in the plane z = -6,…

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Q: A. Solve the following problems using the concepts of Parametric Equations. Show complete solutions.…

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Q: Question 1 Determine whether the integral is improper 5 (x– 4) -Idr Not improper

A: Solving

Q: Q1) A) Find the tangent equation for the function: f(x) = Vx +5 at x-2? %3!

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Q: Q2) Solve the D.E xdy + (2y-x+ 3x)dx 0

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Q: e consider the non-homogeneous problem y" +4y =-32(3x + 2) First we consider the homogeneous problem…

A: We need to solve IVP.

Q: Evaluate the limit, using L'HÔpital's Rule if necessary. sin 3x 1. lim x→0 tan 8x In x5 2. lim x7 –…

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Q: Find the total area of the region enclosed by y=x^2 and y=2x by integrating with respect to y. A…

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Q: Determine the value of 5A+6M if 2x4 + 3x3 +8x2 + 14x + 3 A x-3 х — 3x + M - x(1 + x2)2 1 +x2 (1…

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Q: y = 2 ||

A: We have to find the derivative of the function y = 1-x2ex2

Q: 1+x+y dzdyax Jc JO Jo

A: To evaluate the given iterated integral.