Does the sequence {an} converge or diverge? Explain. Find the limit if the sequence is convergent. n an 6"

Q: 2-use Cramer's rule to solve the system 3tan²x+y=3 2 tan’x -3y=13 X.

A: Given equations, 3tan2x+y=32tan2x-3y=13we know thatfor system  of…

Q: For an integral of the form f sin™(x)cos"(x)dx, saving one sine factor and converting the rest to…

A: Given data÷

Q: Can the Fundamental Theorem of Calculus be used to find 5xcosx?dx?

A: This question can be solved by applying the second part of fundamental theorem of calculus.

Q: 2. Find an equation of the sphere satisfying the given conditions. a. It is concentric with the…

A: In this question, we want to find an equation of a sphere which is concentric with the given sphere.

Q: Find the derivative of the following using First Principle. 1) y = 1 2) у %3D х 3) f(x) = 5x3 %3D 4)…

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Q: Use vectors to show whether or not the points form the vertices of a parallelogram. (1, 1, 3), (4,…

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Q: Which of the following is equivalent to cos 0? cos 0(1+ tan? 0) sin 0 + tan 0 1+ sec 0 O Option 1 O…

A: Checking all options by simplifying.

Q: Direction: Eliminate the following arbitrary constants to obtain the DE. 1. y sinx – xy² = c -

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Q: Which of the following is NOT a solution to the trigonometric equation 2 cot 0 cos 0 – cot 0 = 0? 2…

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Q: What is the amount of material in a hollow cylinder of height 20 cm, given that the sum of the…

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Q: Solve the following items and show your solutions. c.) Find the general solution and solve for the…

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Q: 5. For f(r) = e (x - 5), find a). the domain, b). f', critical points, %3D c). the local maxima and…

A: As per our guidelines, I can answer maximum three subparts of a question. Since you have asked for…

Q: Which of the following expressions represents the height of a right circular cone having a slant…

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Q: O 2y = x In cx?

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Q: The graph shown below is f(x) = 2 cos x. If g(x) = Sřf(t)dt , find g '( 1 ). %3D 4 3- 2- 54 3 2 -1 1…

A: Use the Newton Leibniz Theorem and calculate the derivative.

Q: If 0<c<d​, then find the value of b​ (in terms of c and​ d) for which ∫cd(x+b)dx=0.

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Q: Evaluate by separation of variables. dB du = u(1 – u²) sec 3 O 2u? + sin 28 = C – (1 – u²)² O 2 sec…

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Q: 2. Find the differential equation of the family of circles having their center on the y-axis.

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Q: A number is one more than thrice the other number. What is the minimum product of the two numbers?…

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Q: Solve the given initial-value problems. 4.43. re dr +(y-)dy 0; y(0) 0

A: x ex2 dx + (y5-1) dy =0x ex2 dx =(1-y5) dyvariable separable;∫ x ex2 dx=∫ (1-y5) dyx2=tx dx =dt212∫…

Q: 1-cosx The value of limx→ by using series is 0 sinx True False

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Q: 6.* Sx³ V4 – x² dx - A V(4 – x*)³ – V(4 - x²)* + C C (4 – x²)ª + (4 – x²)5 + C 15 15 D V(4 – x²)³ –…

A: A.=-x23(4-x2)32-215(4-x2)52+Cdifferentiating w.r.t. x;=-x2332(4-x2) (-2x)-2x3(4-x2)32…

Q: 3 dt (2t +8) Vtti

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Q: Evaluate by separation of variables. dß %3D и(1 — и?) sec? р du 2 tan B+ sin 2ß = C – (1 – u?)? 2u?…

A: To solve the given differential equation.

Q: 3- use Cramer's rule to solve the system 8x1-4x2+3x3=0 X1+5x2-X3=0 -2x1+6x2+X3=0

A: Here we have to use Cramer's rule to solve the system.  8x1-4x2+3x3=0x1+5x2-x3=0-2x1+6x2+x3=0

Q: Integral Calculus: Integration by Parts (Original method

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Q: Find f if f(x) = tanh (sin e*). -1 %3D e* Cos e* Cos e* 1- sin? e* | O Option 1 Option 2 e cos e* 1.…

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Q: Evaluate using Linear Equations. v(dx/dv)=6ve2v+x(2v-1)

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Q: the length of a child's square-based jewellery box is 5 cm more than its height. the box has the…

A: Topic  = Algebra

Q: b. S sech x = 2 Arctan(e*) + c

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Q: Solve the following items and show your solutions. b.) Identify if the following functions are…

A: 4.

Q: H.w: Find the Eigen vectors for the largest Eigen value of the system X1+ +2x3=0 3x1-2x2+X3=0 4x1+…

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Q: A ball is thrown into the air and its position is given by h(t)=−7t^2+41t+23  where h is the height…

A: Given the position function of the ball is h(t) = −7t2 + 41t + 23

Q: 3m 5. rad 9. 1.1 rad 13. 1.6 rad 4 6. rad 10. 3.1 rad 14. 2.1 rad 2- rad 3 11. 0.50 rad 15. 0.091…

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Q: dy Find for the following expressions: dx a) y = x5 In(3x) b) y = 2 cos (;+ 2x*) Зx2 + 7х + cos (x)…

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Q: What is/are the critical number(s) of the function S(2) = +4, f(z) :

A: f(x)=x2+4xDifferentiatef'(x)=x2x-x2-4x2f'(x)=2x2-x2-4x2f'(x)=x2-4x2

Q: 1 Use the geometric series 1 >a* for |æ| < 1, to find a power series representation k=0 for the…

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Q: 1 dx V16 – x²

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Q: Find the slope of the line that is tangent to the graph of f (x) 2a-3 at P(3/2, 0) О -3/4 O 2 O (E)…

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Q: Solve the following system of PDES. Uzz = 0, Uzy = 0 0, uzy = 0

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Q: Find k so that the following function is continuous on any interval. S f(x) = 7x 2 < x kx 0 < x < 2…

A: As per our guideline we are supposed to be answer only one question you can repost other questions…

Q: Consider the function f defined on the domain -0.5 s x s 0.5 with f(0) = 1, and 0.5 lim h 0 f(x+h)-…

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Q: dy Find for the following expressions: dx а) y = x³ In(3x) b) y = 2 cos (+ 2x3) X 3x2 + 7x + cos (x)…

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Q: 5. * 1 dx x (In x)3 A 1 + C 2 (In x)² C 1 + C 3 (In x)² 1 + C 2 (In x)2 1 + C 3 (Inx) - - O A O B O…

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Q: Direction: Find the differential equation of the family of curves described. 3. Find the family of…

A: We are asked to find the family of curves of straight lines with slope and `y` -intercept equal.

Q: d) 2х3у + e2y — 4х + 5x2. e) y = (2x* + 4)*x %3D

A: We have to find the derivative

Q: 4. Use L'Hopital's Rule to find (a). lim 22-In 2 3+2z

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Q: 21 claurin series f(x) Also express the serie 1-x %3D

A: Given :

Q: The Maclaurin series for f(x) = x²e=* is E-o(-1)" xn+2 п! False True

A: I am attaching image so that you understand each and every step.

Q: Solve the differential equation with the appropriate method. Finalize answer equated to ky^n.…

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