Given the graph of the function f(x) = cosx, evaluate the following limits: (5 points each) 2x 3T 1. limz-o cosx 2. limx-n COsx *********

Q: Find the radius of convergence of the power series. (If you need to use co or -00, enter INFINITY or...

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Q: Find the interval of convergence of the power series. (Be sure to include a check for convergence at...

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Q: A tank initially contains 10 gal of fresh water. At t= 0, a tap is opened, pouring a brine solution ...

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Q: Solve the initial value problem for x as a function of t.. dx (? - 15t + 56). = 1 for (t> 8), x(9) =...

A: Given that      (t2-15t+56)(dx/dt) = 1 for (t>8), x(9)=0 Here we have to find the initial value p...

Q: Use the following graph and write the shaded area as integrals. A(-1,3) D(2,1) B(0,0) y= h(z) y = S(...

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Q: y = Vx – 7 ,(7,0) -

A: Solution is written in below steps.

Q: Determine whether the following sequence is convergent or divergent. Justify your answer. {1+u^ = w^...

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Q: (y² + x²y + 2x)dx + (x³ + xv+ 1)dy= 0; y(2) = -3 %3D

A: Given: y2+x2y+2xdx+x3+xy+1dy=0, y2=-3 We have to find the particular solution.

Q: If cotx 12 find the other trigonometric functions

A: We will use the basic trigonometric formulae to solve this question.

Q: x + + x -x %3D B.s (9 C-スり(E-メ) E-トE-*ェX S. Let /(x)=x +x+1 and g(x) x-3. Find the following new fun...

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Q: Evaluating Indefinite Integrals Evaluate the integrals in Exercises 37–46. 44. (sec 0 tan 0) V1 + se...

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Q: Question Let k(x) = (-3x² + 2x)g(x)h(x). Given the following table of values, find k' (-2). %3D -2 -...

A: k(x) = (-3x2 +2x )g(x)h(x) find k'(-2) =? k'(x) = (-6x +2)g(x)h(x) +(-3x2 +2x )(g'(x)h(x) + h'(x)g(x...

Q: IUS IIIteTval of Converger Approximate In(0.5) using the first 5 terms using the expansion.

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Q: Consider the integral 2n* g(x) dx . There is a function g(x) such that when u = In x the resulting i...

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Q: Solve using the U-Technique Question 10 For ſk*e3*dx = 1 (ke)3x 3 (1–In 2-1) If u = 3x, then k =? .....

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Q: prove that tanx = V secxsinxtanx %3D

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Q: Find the derivative of y with respect to v. y = In (cosh (2v)) – tanh? (2v) The derivative of y with...

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Q: " + y = 12 cos 2x - sin x. A. " + y = sin 3x +4 cos x. A

A: Given: y''+y=12cos2x-sinx

Q: 0. Refer to Problem 19: How fast is the circumference of a circular ripple changing when the radius ...

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Q: Solve using the U-Technique Question 8 Given: S . There is a function f (x) such that when u = -x³, ...

A: Given: ∫2f(x)dxe-x3   , u=-x3

Q: Find the indefinite integral. (Use C for the constant of integration.) 9. dx XV 81 - (In x)2 |

A: Here we will solve the given integral,

Q: Use the ratio test for absolute convergence to determine whether the series converges or diverges. I...

A: ∑n=1∞-23k

Q: Sy = 4 +

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Q: prove that tanx V secxsinxtanx

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Q: If cotx 12 find the other trigonometric %3D functions

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Q: Determine the area and circumference of the following circles. 17. 18. 19. 5 in 5 in 28 cm

A: Area and circumference of a circle

Q: Use any method to determine whether the series converge. 1 (a) E k=1 k' + 12k + 1 This series conver...

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Q: Evaluate the following indefinite integrals. 1. Jx²dx 2. S(x³ + 2x)dx 3. S(a)dt :a = constant

A: Solving the problem by finding the indefinite integral.

Q: oblem Set C 2x+3 Find the domain of the function H(x) .3 x'-4x %3D

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Q: Let f dx be given. if u = e* + 1, then the resulting integral is f(u) du. Compute f(3) 2/3

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Q: Question The position of a car traveling along a highway is given by the function s(1) = 21° – 10t2 ...

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Q: Determine the derivative of f(x) = ( In x )6 with respect to x. f'(x) =

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Q: (ke) 3 (1-In 2-) 1. For Sk*e3* dx = +C.f u= 3x, then k=? 2.

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Q: 00 (-1p+1 Imestigate for convergence or divergence. e) Diverges by IntegalTest (b) Converges by Alte...

A: solution:-∑n=1∞-1n+1nan=1nan+1=1n+1Applying Alternating series testan>0an>an+1limn→∞an=limn→∞1...

Q: Solve the initial value problem. d²y = 2 e -X, y(0) = 0, y'(0) = 4 dx

A: ∫ d2ydx2 =∫ 2 e-x dxdydx=2e-x(-1)+Bdydx=-2e-x+B ...(1)

Q: Evaluate the following integral. Sesim (5- In 2 dx 3

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Q: Evaluate the limit below. 1 lim (x,y)→(0,0) 1-x2-y?

A: limx, y→0, 011-x2-y2

Q: Evaluate the da xp: 1+z VE- Arctan()+C O b. 2/T+2Arctan(V)+C Va - 2 Arctan(ya) +C O d. 2 7-2Arctan(V...

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Q: Set up a definite integral with respect to x (dx) (set up only, do not evaluate the integral) to fin...

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Q: Solve the initial value problem. dy + 5xy = 8x, y(0) = - 6 dx y =

A: topic - differential equations

Q: H.W Find the Adjoint to the following matrix 0.5 01 X = -1 1 -0.8 2.2 2 -3.3

A: Let A =[ aij ] be a square matrix of order n. The adjoint of a matrix A is the transpose of the cofa...

Q: Find the indefinite integral. (Use C for the constant of integration.) 2 cosh(x) dx

A: Evaluate the integral∫2coshxxdx

Q: DETERMINE IF THE FOLLOWING FUNCTION IS CONTINUOUS AT THE GIVEN VALUES OF X.  f(x) = 1/x^2 - 9  a. ...

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Q: Plot and label the following polar point on the graph. Find the Cartesian coordinates of this point....

A: see below the answer and explanation

Q: if we let u-4x- 1 for the 2 tan(4x-1)-3 cos (4r-1) dx, what will be the resulting integrand? cos 4x-...

A: The given integral is  (2tan(4x-1)-3cos2(4x-1))/cos(4x-1).

Q: In Exercises 17–56, find the most general antiderivative or indefinite integral. You may need to try...

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Q: If cotx 12 find the other trigonometric functions

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Q: Solve using the U-Technique Question 15 Given: S 5x? cos 3x³dx. If u = 3x³, then the resulting integ...

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Q: 9=1-5t Gas. d= o ans

A: As per the guidelines when multiple question are posted in single pic  then we are supposed to solve...

Q: O Define f (x) = 1x = Graph it. Label as a piece wise defined function your graph.

A: Given