1) Write the next four terms of the sequence: {42, 35, 28, 21, ...}. Express the nth term of the sequence.

Q: A man borrows Php 100,000 from the Social Security System for a term of one year. The interest…

A: Bank Discount  =100000×15100=15000

Q: Find the arc length L of the graph of r(t). r(t) = 4 cos(t)i + 4 sin(t)j+ tk, 0<t< 2m L

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Q: 6x7 – 5Vx + 3x + 4x-2 dx

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Q: Match the vector field with its graph. F(x, y) = xi + 3yj 5 y -6+

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Q: Given that i = and i = and that i • v = 188 determine the value of the constant A.

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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: f(x)=x-4/x^2+2x+17 What monomial expression best estimates the behavior of x-4 as x→± ∞ ?…

A: Given problem:- f(x)=(x-4) /(x2 +2x+17)    What monomial expression best estimates the behavior of…

Q: 9. S sec 2x dx 10. S cos x esin x dx 11. dx x+1

A: Evaluation of the above integration is

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: Starting at age35 ​, you deposit​ $2000 a year into an IRA account for retirement.  Treat the yearly…

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Q: 1. Identify the type of conic section whose equation is given, then find the vertices and foci.…

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Q: Question 2 Find the equation of the line through (9, 2) with slope -2/3. Select your answer y =-2/3…

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: Find Inz3 dz

A: LetI=∫lnz3zdzLet z3=udifferentiate 3z2dz=duDivide 3z2 on both sidedz=du3z2dz=du3z2Divide z oboth…

Q: d d Calculate r1(t)· r2(t)] and ri(t) × r2(t)] first by differentiating dt dt the product directly…

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Q: 2. A triangle is inscribed in an ellipse whose equation is 9x? + 16y? - 216x- 320y+ 2320 = 0. One…

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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: dy Q4) Find for the following functions dx 1. y = 2x? + e2x-1 2. y = sec x tan x 3. y = t2 + 2t t =…

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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: 1 2 1 | | (x² + y»2 + z²)dzdydx lo Jo

A: To evaluate the given triple integral: ∫-10∫02∫01(x2+y2+z2) dz dy dx=∫-10∫02∫01(x2+y2+z2) dz dy…

Q: Q2) Find the integral value for the following functions dx 4. S x2Vx2-1 ecos-1x -xp- V1-x 5. S 6. Se…

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Q: Write the standard form equation for a hyperbola with center at the origin, vertices at (0, 6) and…

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Q: Q2) Find the integral value for the following functions (choose five only): 3x dx 1. JJ+3x2

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

Q: Find S(sin20cose + cos30)d0

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

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Q: Find a formula for the nth term of the sequence (choose one of 2) The sequence 2,6,10,14,18, ..

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: 12. L(s? – 1) sds 13. (1² – #) dt

A: ∫xndx=xn+1n+1+C , C is a constant for any real number n.

Q: at x = 2 for the function below. dx Evaluate y = - 5u? + 4u + 9, where u = 9x2 – 2x + 4 Answer…

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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: 4. The dimensions of a rectangle are measured to be 8 ± 0.1 by 4 0.2 inches. What is the approximate…

A: Let's find.

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

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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: Use an appropriate definition to prove the following limits. x³ – 16x* = 1 I+0 r°+ 4x² x +2 V9x2 + 4…

A: This is a problem of limit . Based on the formula and concept we will answer the question.

Q: Find a power series representation for the function. (Center your power series representation at x =…

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Q: Verify Green's Theorem by evaluating both integrals dA v? dx + x2 dy ax for the given path. C:…

A: We have to verify the green's theorem

Q: Find T(t) and N(t) at the given point. r(t) = (t – 2)i + tj; t= 2 T(2) = N(2) =

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Q: Example: Find C² sint]? Solution:

A: To solve the following problem

Q: 3. Find the absolute maximum value of the function f(x)=- 1+x2

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Q: Q15. Find the Maclaurin series representation for each of the following functions. For each series:…

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

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Q: Find the arc length L of the graph of r(t). r(1) – ittj Vor? k. 1 r(t) = t i+tj 2 <t< 5 L = i

A: To find the arc length L  of the graph of r(t).

Q: ||r(t) x r"(t)|| ||r'(t)|³ Use the formula k(t) to find k(t). 13 r(t) = 4 cos(7t)i+4 sin(7t)j+ 3tk…

A: A detailed solution is given below

Q: Evaluate the indefinite integral. x2 dx 0.2x3 + 2.7 + 2.7

A: topic - indefinite integral

Q: B) Find the limits by using L.Hopital rule : 7x 1. lim x-0 sin 2x х2-16 2. lim x-4 (Vx+5)-3

A: Given; (1). limx→07xsin2x

Q: An airplane with an airspeed of 80 meters per second is due east, gaining altitude, and has a line…

A: Let us sketch the situation roughly using these following information: N = North, S = South, E =…

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: The acceleration function (in m/s²) and the initial velocity v(0) are given for a particle moving…

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Q: 4 '2 If f is continuous and f(x) dx = 10, find | F(2x) dx. %3D

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Q: Q1 Using a method of reduction to separable equation and reduction to linear equation, find the…

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

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