Sketch the region enclosed by ?=5?y=5x and ?=3?2y=3x2. Decide whether to integrate with respect to ?x or ?y, and then find the area of the region.

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

A: Given query is to find the integral.

Q: Find the sum of the first 100 terms in the arithmetic series 1+2+ 3+4 + ... + 100.

A: To find the sum of first 100 terms of given arithmetic  series.

Q: Let B be the sphere x2 + y? + z? = 1. The volume of the portion of B contained in the first octant…

A: Here, the sphere is x2+y2+z2=1 to find the volume formula for the spherical coordinates of it in the…

Q: here the curves intersect, draw a sketch of them.

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Q: At which of the given numbers, the following power series is divergent? 10" x" n! n=1 O a. None of…

A: Ratio Test : Suppose we have series ∑ an.Define, L =limn→∞ an+1an , then(i)  If L<1, series…

Q: - If f(r) = e² is a solution of xy" – (r + 1)/ + y = 0. Then, the general so (A) y = c1e² + c2e=z…

A: Answer is in next step     option  E is correct.

Q: aluate the function. Give the exact value. cos tan(V3) -1 cos(arctan( V3% = 0.5

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

Q: Consider the differential equation r'y" +3ry'-3y 2a - 3r. of variation of parameters to solve the…

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Q: x-1 8. y = log х+1

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Q: dx J Vx² – 25

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Q: Integrate using any applicable method. Be sure to give an exact answer. (3z+1) Enter your answer in…

A: Solve the following

Q: 10. y = (e3x+4 +2)/(e2*3x +1)

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Q: (1) lim (In ) = z (x1 (j) lim rsin z x→0+ sin 2x + 2 arctan 3x + 3x2 (k) lim x→0 In (1+3x + sin? x)…

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Q: Evaluate the double integral over the given region. |6x sin xy dA, R. 0 SxsA, 0sys1 R. O A. 6x 兀 OB.…

A: We will evaluate the double integral.

Q: 3 - 6t +1 x =ť° +• ;teRat t= 4 y=t° - 3t² – 9t –1

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Q: 2 5. Given cos a =- and tan ß =- 2 575BS7, determine the exact COs a value of: a) cos(a + B) and b)…

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Q: Determine any critical point(s) for the function f(x)=  -3 / x2 - 9

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Q: Find a formula for the nth term of the sequence. - 1, 4, - 9, 16, -25, .. Determine the sequence's…

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Q: Use the transformation u = 4x + 3y, v = x + 3y to evaluate the given integral for the 4 4 region R…

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Q: Use Intermediate Value Theorem to explain why the function has a zero in the given interval. [0. 1]…

A: The Intermediate Value Theorem: If f be a continuous function over a closed interval [a, b] with its…

Q: Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve.…

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Q: ind the values of a and b so that the function = x + ax + b has a local maximum at the (-16,- 12).

A: We will find the value of a and b.

Q: Find the general equation of the tangent plane to the surface x2 + y2 −2xy −x + 3yz = −4 at the…

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Q: (3) 2x Find the linearization L(x,y) of the function f(x,y)= e cos (3y) at the points (0,0) and 0,…

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Q: 3. Out of frustration, Maxine throws a stone into a river. This caused ripples in the form of…

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Q: Calculus What is the inverse of f(x)= x^3 +x -4

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

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Q: Determine the exact value of 2 sincos cos 12 12

A: Given query is to find the exact value of the expression.

Q: Ryan is puréeing different fruits and freezing the purées in ice cube trays. He knows that the…

A: Volume of each frozen cube = 1.5 cubic inches. We have to find the volume of the kiwi fruit and then…

Q: II. Find the Inverse Laplace of the following 2s-9 d. s2 +2 1 е. (s²+1)(s²+4s+8)

A: We have to find the inverse laplace transform.

Q: Use Lagrange multipliers to find the given extremum. Assume that x and y are positive. Minimize f(x,…

A: We have to minimize the given function.

Q: a. (csc 0)(1+ sin² 0 + sin 0 cot? 0) d0 5.

A: We will solve the integration

Q: The graph of a function f is given below. According to the graph, the derivative of the function…

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Q: What are the two values of k closest to 1 - 4 for which S sin? (x +4) – cos² (x + 4) dæ has a value…

A: The solution is given in the next step.

Q: Find the nth Maclaurin polynomial for the function. f(x) = sin(x), n = 6 Po(x) =

A: nth Maclaurin polynomial for the function f(x) :       Pn(x) = f(0)+f'(0)x +f''(0)…

Q: Are the Following Vectors Linearly Dependent or Independent? 3) (0,1,0), (2,1,0), (3,4,7) Ans.…

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Q: 1. a. Show that two lines with direction vectors d (2,3) and d, (6,-4) are perpendicular %3D b. Give…

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Q: Calculate the trapezoid approximation of 5dx using four subintervals. O T5 = 0.60 O T5 = 0.40 O T5 =…

A: The trapezoid approximation of the given integral is given below.

Q: sin(x?) Evaluate lim 1+0- e2r – 2x – 1°

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Q: dªy d³y -4. dx4 „d²y -6· dy dx3+ 7 + 2y = e-* + xe¬× dx dx2

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Q: 2x J(x – 3)2 A = 6, B = 2 A = 2, B = 6 A = 2, B = - 6 A = - 2, B = - 6 A = - 2,B = 6 None of the…

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Q: A. Find the area of the plane region bounded by the given curves 1. y = x, y = 2x, and x +y = 6…

A: Note: As per our guidelines we are restricted to solve only one problem. Please upload separately…

Q: d3y +6° dx2 d²y d- dx3 15 dy 15 dx 100y = 0 - - %3D

A: Given :d3ydx3+6d2ydx2-15dydx-100y=0

Q: Which of the following is the particular solution of a nonhomogeneous differential equation…

A: Here, given that: yc=c1x2+c2x3⇒y1=x2, y2=x3 And, u1=2x-3x2, u2=2x+3

Q: The function x2 f(x) 1 - x is decreasing on (0, 1). Select one: O True O False

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Q: 13. A population of yeast cells can double in as little as 1 h. Assume an initial population of 80…

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Q: Find a power series representation for f (t) = ln(10 – t). %3D

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Q: Q5: S x dx ajconverges to 1 bjconverges to cconverges to- 4. d)diverges 25-2

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Q: 4. y = x, y = 2x, and x + y = 6 (Answer: 3 s. u.)

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Q: Find all values of x for which the series converges. (Enter your answer using interval notation.)…

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