Let u = 10TX. The differential of u with respect to x is du = 1072 20 7 Step 2 Rewrite the integration in terms of u. 1 x cos 10Tx2 dx = COS u 20T du 20. T Apply the constant multiplication rule on the right side. 20T COs u du 20-元 Step 3 Integrate the right side. sin(10x sin(u) 20 + C Cos u du = 20 20T Step 4 Substitute the expression for u on the right side, and obtain the integral. X cos 10nx² dx = Submit Skip (you cannot come back)

Q: *e「ス+

A:

Q: equations

A:

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

A: y=∫cos412x dx

Q: k + 1 2(- 1)k+1 5k + 1 k=1 The series diverges. O The series converges.

A:

Q: k E(-) k=1 If p = + 0, enter "inty". II

A:

Q: Q1) Evaluate the following integral using By Parts Method: х.In(x3 + x) dx

A:

Q: Find each limit in Problems 37-60. Note that L'Hôpital 's rule does not apply to every problem, and ...

A:

Q: Using u-substitution, the integral f(x)dx reduces to a new integral f g(u)du. If g(u) : u+1 evaluate...

A: ∫f(x)dx = x + ln(x-1) +c we have to find f(x) so we have to derivate the ∫f(x)dx so f(x) = 1 + 1/(x-...

Q: xdy +(y– xy+2)dx = 0

A: The given differential equation is; xdx+(y-xy+2)dy=0

Q: Solutions of differential equations: y' = sin x O y = - cos x +c O y = cos x + c %3D

A:

Q: A Complete the table. du formula answer 24x +2 (2x -1) (Ax + 2)3 d 2. 7Vx - Sx de Se 3nin2 de sin S ...

A:

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

A:

Q: Evaluate the integral. In(10 x 9) dx +C

A:

Q: 1. The standard form of the general first order linear differential equation in y is 2. The linear d...

A:

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

A:

Q: A statue 3 m high is standing on a base of 4 m high. If an observer's eye is 1.5 m above the ground,...

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

A: The given series is: ∑k=1∞k!k8 Let, ak=k!k8; k≥1

Q: Find the unit vector of A=3ax+2ay-3az

A:

Q: 1. Given: az = 12, a3 = 24 Find: ao =? а. 2 b. 4 с. 3 d. 5 2. Given: a, = 16, a, = 1024 Find: a, =? ...

A: 1)  a2=12 , a3=24    Since the terms are in geometric progression    ⇒a3a2=a2a1=a1a0=rconsider a3a2=...

Q: an exponential function y f(x). (2,8.64) (1,7.2)

A:

Q: 4. Fond theequation ofthe tangent line to the graph of the Function FCx)=R-JX at the point (1,0).

A:

Q: Evaluate the integral using tabular integration by parts. 4 x V2 x +1 dx +C %3D

A: LetI=∫ 4x32x+1dxPut 2x+1=u2x=u-1x=u-12differentiate 2dx=dudx=du2I=∫ 4u-123udu2I=∫ 4u-138udu2I=∫ 14u-...

Q: Solve using the U-Technique Question 14 Let dx be given . If = e* + 1, then the resulting integral i...

A: Solving the problem by finding the value of f(3)

Q: Find the radius of convergence and the interval of convergence. 2* k=0

A:

Q: Determine f(x) so that cos(In²x) f (x) dx = sin(In²x) + C

A: Let t =log2 x and follow step 2nd . 

Q: Find the derivative of f(x) = sec(tan(x) + cot(x))

A:

Q: Question 2 If S(16x4 – 16x³ + 4x²)dx = F(x) + C, then F(x) 16 A 5 4 x3+4x4 3 B (4x² – 2x) 3 16 4 x3 ...

A: The given integral is 16x4-16x3+4x2.

Q: a. 2 sec (5x²) tan(5x²) + C b. tan (5x) + c c. 10 tan (5x) + c d. none of the above 27. Evaluate csc...

A:

Q: dx 6. Evaluate 5-16r

A: Evaluate ∫dxx83-16x2

Q: The integral / 2cos(2')dr takes the form & cosar du when =2 and/(x)=x-5 What is the value of (+2)? 2...

A:

Q: Find the exact value of the trigonometric function. (If an answer is undefined, enter UNDEFINED.) 19...

A:

Q: Evaluate f(3v+ dx

A: As per our guidelines we are only solve one question (i.e. the first question from start) and the re...

Q: Find the indefinite integral and check the result by differentiation. (Use C for the constant of int...

A:

Q: 12. Evaluate ((1– cos x) dx a.) 1- sin x +C b.)x - cos x +C c.) 1- cos x+C d.) x- sin x+C 13. Evalua...

A:

Q: 5 In(x); xo = 1

A:

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

A:

Q: Use the Quotient Rule to find the derivative of the function. Re) = Sos(t) f'(t) =

A: We will find the derivative of the function f(t) as following.

Q: a. When Frank initially sees the coyote, the angle of depression for his vision is 6 degrees. Draw a...

A: Frank stands at the top of a cliff. On the ground 310 feet below, frank spots a coyote.

Q: The integral / 2/ (*) cos(2*) dx takes the form k cosu du when u=2* and f (x) =x – 5. what is the va...

A:

Q: Evaluate f-4*3 dx In4 b,- -3in4 +C C. In 64 d. none of the above Evaluate f4x cosx dx a. sin x + C b...

A: As per our company guidelines we are supposed to answer only first 3 sub-parts. Kindly re-post other...

Q: Find the exact value of the expression, if it is defined. (If an answer is undefined, enter UNDEFINE...

A:

Q: 2. @-2-6X8-マメーメー3メー6時+2

A: f(x,y) = 2x2-3y-4∂f∂x =ddx(2x2-3y-4)∂f∂x=4x∂2f∂y∂x =ddy(∂f∂x)∂2f∂y∂x =ddy(4x)∂2f∂y∂x =0∂2f∂x2 =ddx(∂...

Q: A cylindrical tank with radius 7 m is being filled with water at a rate of 3 m/min. How fast is the ...

A: This question is based on application of derivative.

Q: 5. if we have two polynomials pl=3x5 + 8x* – 2x2 + 4x + 1 p2= 2x6 + 3x* – x² + 4x Find:- Your answer...

A:

Q: Find the Maclaurin polynomials of orders n = 0, 1, 2, 3, and 4 and then find the nth Maclaurin polyn...

A: Please see the below picture for detailed solution. 

Q: dx The integral S reduces to S k, where u = f(x) and for some constant k . Compute f(1). ex+1

A:

Q: Q3) Find the limit for the following function by using L'Hopital's Rule: x2. e* lim x→0 tan2 x

A:

Q: Classify the series as absolutely convergent, conditionally convergent, or divergent (-1)*+1 5k

A:

Q: (x – h)? + y? = r² O y " +(y')² + 1 = 0 O y" +(y')² = 0

A: