Use Part 2 of the Fundamental Theorem of Calculus and the following formula to find the derivative. g(x) d. f(t) dt = f(g(x) g'(x) dx sin(z) d. dt %3D dx 1+ t10

Q: 9. Evaluate f(e* + 2*) dx a.) 2e* + +C In2 b.) er + 2ln* + C c.) e* ++c d) e* + 2ln x + C In2 10. Ev...

A: Evaluate integrate. And follow step 2nd .  According to guidelines we solve only first three parts. 

Q: Use the ratio test to determine whether the series converges. If the test is inconclusive, then say ...

A:

Q: A. Describe the set of inputs, the function rule, and the set of outputs for each function. 1. The a...

A:

Q: Find the general term of the sequence, starting with n = 1. Determine whether the sequence converges...

A: The given sequence,      17, 179, 1792, 1793,......

Q: Determine whether the series converges, and if so find its sum. If the series diverges, indicate tha...

A:

Q: k(k +7)

A:

Q: Classify the series as absolutely convergent, conditionally convergent, or divergent. Σ (-1)*+1 k7/6...

A:

Q: The function f(t) = 5(1.3)' determines the height of a sunflower (in inches) in terms of the number ...

A: As we know that; The average rate of change between the interval t1≤t≤t2 is given by; Average rate o...

Q: S(z) = 64 –3 V/

A: f(x) =x964-x3We can rewrite the function as;f(x) = x9  164-x3f(x)=x9 (1641-x364)a=164,  r=x364   (Ge...

Q: fy re aris Find volume

A:

Q: 1- 8x + 72(-1) (k + 7)! k! k=2

A:

Q: f(x) Find g(3) given that f(3) = -6, f'(3) = -4, and 9(x) = |3| 8 Answer: 5

A:

Q: A pair of parametric equations is given. x = Vt, y = 9 t (a) Sketch the curve represented by the par...

A:

Q: What is the value of? df where xez+1 da (0), f(x) = %3D 1+e-z Write your answer as an integer or as ...

A: topic - derivative of a function

Q: solve question 32 with complete explanation asap

A: Topic:- complex number

Q: #1 only

A: Topic:- differential equations

Q: Use the formula for the binomial series: (1 + x)" = т(т-1) 2 2! m(m–1).-(m-k+I),k + + 1+ mx + %3D .....

A: The maclaurin series for 1+x7

Q: 20. y + x + 4 = 0; (-2, 2) %3D

A: Topic = Derivative

Q: Consider the following sequence: {a, } = {n – n² }= Use an+1 - an to show that the given sequence {a...

A:

Q: a. When the observer initially spots the ship, the angle of depression for the observer's vision is ...

A:

Q: 4 -4 -5- Find the parametric equations for the graph shown above given that when t = 0 the point on ...

A:

Q: Q5) Use the Chain Rule to express dy /dx in terms of x and y: y = csc t аnd x = sec-1 t

A:

Q: Evaluate the integral. x2 e dx +C

A: Here, to evaluate: ∫8 x2exdx=8∫x2exdx

Q: Q6) Evaluate the following integral by using Odd and Even Powers Method: y = cos* (;x) dx

A: y=∫cos412x dx

Q: Evaluate the integral J x cot x² sin(in |sin x²l) dx.

A:

Q: Use the Laplace transform to solve the initial value problem below: b) y" + 3y' + 2 y = f (t) Where ...

A:

Q: Q5) Use the Chain Rule to express dy /dx in terms of x and y: y = csc t аnd x = sec-1t

A:

Q: ,2 30. lim x In x

A: Topic = Limits

Q: Use the difference an+1 – An to show that the given sequence {a, } is strictly increasing or strictl...

A:

Q: Eliminate the parameter to find a Cartesian equation of the curve. x(t) = 101nt y(t) = Vi (a) Cartes...

A: We need to eliminate parameter and find range for a and y.

Q: Find the radius of convergence and the interval of convergence. k +8 Radius of convergence: Interval...

A:

Q: create a graph with labels of a function that have one point where f(x)=-3, at least one local minim...

A:

Q: Question 1 For each of the following, determine whether the given SEQUENCE converges or diverges. If...

A:

Q: 1. S(z) = 64 –³ VI 2. -12r2 S(z) = 1+ 8x²

A:

Q: Find the volume under the paraboloid  z = 4x2 + 4y2,  above the xy-plane, and inside the cylinder  ...

A:

Q: Use the difference an+1 an to show that the sequence {n – 8"} +oo In=1 is strictly increasing or str...

A: The sequence{n-8n}n=1∞

Q: Given: a2 10, az 13 Find: a, =?

A: Solution is written in below steps.

Q: Find the general term of the sequence, starting with n = 1. Determine whether the sequence converges...

A: Given

Q: Find the derivative of the function without using the Quotient Rule. y = 63 8(x)10

A:

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

A:

Q: 2.ly-x dx+ dy = 0

A:

Q: (2х — Зу + 2)dx - (3x + 4у-5); У-3) %3 4 |

A:

Q: Determine whether the alternating series converges. 51n k | k k=3 O The series converges. O The seri...

A:

Q: Given A=-3ay +2ax +4az, B=3az -2ay + 5ax and C=-3ax +4az +5ay. Find a. A+2B-C and b. I 2A-3B+C I.

A: Given A=2ax-3ay+4azB=5ax-2ay+3azC=-3ax+5ay+4azA+2B-C=2ax-3ay+4az+10ax-4ay+6az--3ax+5ay+4az          ...

Q: . The standard form of the first order linear differential equation x y'+xy +2 = 0 is,

A: This question is based on to form a standard first order differential equation.

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

A:

Q: k-1 Since the series can be rewritten in the form > 4- (). it is a geometric series with: k=1 a =

A:

Q: A straight river flows east at a speed of 8 mi/h. A boater starts at the south shore of the river an...

A:

Q: Determine whether the series converges using the Ratio test. Σ 4* k8 k=1 The series

A: Given query is to find series converges or diverges.

Q: EXERCISES 1. What value(s) of c, if any, will satisfy the IVT for the given function f and the given...

A: topic - intermediate value theorem