Find a formula for the nth term of the sequence in terms of n. 1 3 32 33 34 4' 6' 8' 10' 12 an = | for n21

Q: Find the limit. lim (t i - 7 j+1² k) t-5 lim (t i - 7j+ k) i+ i j+ i

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Q: Use the alternate definition, lim Ax)-Aa) to determine the instantaneous rate of X- a change of Ax)…

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Q: b) Solve the given homogeneous differential equation subject to the indicated conditions. y" + 2y' +…

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Q: The total sales of a company (in millions of dollars) t months from now are given by S(t) = 0.02t° +…

A: This question can be solved using the concept of interpretation of a function and its derivative at…

Q: у" - (а + В)у' + авy %3D 0

A: Given

Q: m²-m Find S (m1) dm

A: Given; I=∫m3-m-1mdm   As we know that; The Sum rule; ∫fx±gxdx=∫fxdx±∫gxdx The Power rule;…

Q: 0. xe-4x dx 1 dx x(ln x)3 4

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Q: 15. S(x + 2)²dx

A: Solve the following

Q: Find the area of the region bounded by: r 9 cos(80) 0 < 0 < 2T

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Q: DEFINITION 7.1.1 Laplace Transform Let f be a function defined for tN 0. Then the integral L{f{t)}…

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) a + bxº dx 10ax + bx10

A: Evaluate the indefinite integral

Q: ||F(t) × r"(t)|| ||r(t)||* Use the formula k(t) to find k(t). r(t) = t’i+ t®j K(t) =

A: See the answer below

Q: Given the e dz nd y, find ar

A: Given: xlny=zArctan3zy

Q: Evaluate 2x(x2 + 2)*dx

A: First I have used  a substitution and made integral easy and then solved it.This is the process.

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: 4. sec 4x tan 4x dx

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Q: Solve the following problems. 2. At 1:00P.M, a thermometer reading is 70°F is taken outside where…

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Q: A tank in the shape of an inverted cone has a height of 15 meters and base radius of 4 meters and is…

A: Dear learner, As per our guidelines we can provide the solution for first one only. Kindly post…

Q: 2x + 6 Consider the function f(x) = . For this function there are two important intervals: (– ∞, A)…

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Q: 5. y = [csc Jarcsin (cos.x)

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Q: Q4) Find for the following functions (- dx Зх +4 %3D 2x+3 6. y = tan-1 V4x3 - 3 %3D

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Q: Determine equation of the line in vector form, parametric form, symmetric form and scalar equation…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the area inside the loop of the following limacon: r = 8 – 16 sin 0

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Q: na the coordinates of a point P on th line and a vector parallel to the lihe. x - 2 - y + 5 = z + 4…

A: Given query is to find the coordinates of the point p and vector v.

Q: Let й —, i = where A and B are some constants. Given that ủ + 40 = find the value of the product…

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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: Find the length of the spiraling polar curve 2e 40 From 0 to 27. The length is

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Q: Evaluate the definite integral. e14t i + e¬1j +t k )dt O el4 (e-- – 1) j + k i+ 14 (el4 – 1) i- (e -…

A: Evaluate the definite integral

Q: Question 3 Find the area enclosed by the curves y y = 2 V1- 9x2 O V5- 9. 2n B 3 5n D 6

A: Solution is given below:

Q: Find the area of the region outside r = 5 + 5 sin 0 , but inside r = 15 sin 0.

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Q: t the end of 8 years, Beth will have approximately S Do not round until the final answer. Then round…

A: Use half yearly compounded formula.

Q: Find the integral value for the following functions

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Q: ||r'(t) × r"(t)|| ||r'(t)||³ Use the formula k(t) = to find «(t). r(t) = e""i+ e'j K(t) =

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

A: To find the area between the line and x axis.

Q: The population of mosquitoes in a certain area increases at a rate proportional to the current…

A: Given that the population of mosquitoes in a certain increases at a rate proportional to the current…

Q: dx メ-1

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Q: Consider vectors U and V with magnitudes |U= 55 and | = 70 units, separated by an angle of 90. Let I…

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Q: Find the exact length of the polar curve described by: r = 9e-0 5 on the interval -T <O<67. 6

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Q: For the following: a) Determine the intersection points. b) Draw a sketch of the graph. c) Find the…

A: We can solve this as follows:

Q: Use De Moivre's theorem to solve for z given z = 3 – 2i. Write your answers in rectangular form. Use…

A: Given: z5 = 3-2iz   = 3-2i15                                     1-------------------De-Moivre's…

Q: Find the exact arc length of the curve over the stated interval. y = 3r/2 – 4, from a = 0 to a = 1…

A: This question can be solved using the formula of arc length.

Q: An oil tank is being drained for cleaning. After t minutes there are Vlitres of oil left in the…

A: This is application of derivative problem

Q: APPLICATION I. Find the antiderivatives of the following functions using the substituion rule. Write…

A: Solving the problem by finding the value of the integrals.   NOTE :: As per our Expert guidelines we…

Q: Use Green's Theorem to evaluate the line integral. 2xy dx + (x + y) dy C: boundary of the region…

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Q: 3 Ay 10- Find equation of tangent line at the point (0, 7) for Cos (7x - y)

A: Solving

Q: Write the 4 x 4 elementary matrix which accomplishes the row operation R3 - 5 R2 ---> R3 when you…

A: let  I be the 4×4  identity matrix I=1000010000100001

Q: Write an equation for the function graphed below. Use the smallest powers possible to meet the…

A: To find the equation of given graph.

Q: dy + 2(t + 1)y? = 0 dt b) Solve ;y(0) 8

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Q: If 10% of a radioactive substance disintegrates in 4 days, what is its half-life

A: Follow the procedure given below.

Q: S csc2xdx cosx O sinx+C O -cotx+C O -cotx

A: By using standard formula.