Tutorial Exercise Find the indefinite integral. sin 70 V cos 70 de Step 1 To solve the integral sin 76 V cos 78 de, rewrite the integral as 3 sin eV cos 70 sin 70 de. Use the trigonometric identity sin? e + cos? = Therefore, sin 70 Vcos 70 sin 70 de cos 70 sin 9 de.

Q: Q5) A) Graph the curve Y = - 2 x (x -4)(x + 6)(x - 2) between the value of x [0, 4), then find the a...

A: The curve y=-2xx-4x+6x-2 between the value of x∈0, 4

Q: Express the given quantity in terms of sin x and cos x. Sin (2n – x)

A: The given quantity is  sin(2π-x)

Q: L{f(t)g(t)} = L{f(t)}L{g(t)}, where both f and g are continuous and of exponential order. True False

A: We have to find the reason

Q: Find an explicit solution of the given initial-value problem. 1 V1-у? dx - V1-x2 dy — 0, У(0) y =

A:

Q: Use sigma notation to write the Maclaurin series for the function 17 In(1 + x) k =

A:

Q: ) Graph the curve Y = x (x +5)(x -3) between the value of x [-5, 3], then find the area of the finit...

A: Area under the curve =∫ab(upper curve -lower curve)dx  

Q: Graph the parabola, then label the vertex, axis, and intercepts. 1 Y = --x² + 2x + 4 %3|

A:

Q: 9)6

A:

Q: Knowing that the vector field given by the image function is conservative, determine its potential f...

A:

Q: Find the Taylor polynomials of orders n = 0, 1, 2, 3, and 4 about z = x0 and then find the nth Taylo...

A:

Q: bicycle wheel has radius R. Let P be a point on the spoke of a wheel at a distance d from the center...

A: Find your answer below 

Q: A rectangular lot which has an area 120sq.m will be divided into two portions such that the product ...

A: A rectangular lot which has an area 120sq.m will be divided into two portions such that the product ...

Q: For the sequence {an}, with lim an = 9, this means the terms in the sequence approach 9 as n becomes...

A:

Q: ek is convergent or Use the Integral Test to determine whether the scries 1+e2k k=1 divergent. Remem...

A: For integral test, f(x)=ex1+e2x. Now,               ∫ex1+e2xdxLet  u=ex.=∫11+u2du=arctanuSubstitute ...

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

A: Topic:- sequence and series

Q: Problem 2: A piece of string whose length is given below is cut into two pieces. One piece is used t...

A:

Q: Consider the function g : (6, 0) → R given by, 3x g(x) : x-6 Then we have that lim g(x) =3 . %3D x→∞...

A: The given function is: g(x)=3xx-6&limx→∞g(x)=3

Q: 25łn²(x) log (x) dx

A:

Q: 5. The sum of the first 12 terms of an arithmetic series is 186, and the 20th term is 83. What is th...

A:

Q: df Find dx by using chain rule if f = u =-1 , x=-1 u+1

A:

Q: Assume that C(x) is in dollars and x is the number of units produced and sold. For the total-cost fu...

A: We have to find ∆c and c'(x). 

Q: 2. f(x) = (8x³ – 7x)(7x¬ + 5x³) at x = -1

A:

Q: Find all angles 0 between 0° and 180° satisfying the given equation. Round your answer to one decima...

A: We can use the formula  θ=sin-1ab and sinθ=sin(180-θ) to solve this equation

Q: Find the volume formed by rotating the region enclosed by * = 11y and y = ¤ with y > 0 about the y-a...

A:

Q: 11. If f(x) = x² + x + 1 and g(x) = x – 3, find the following. (a) f+g (b) f – g (c) fog (d) gof (e)...

A:

Q: Determine f(x) so that cos(in?x) f(x) dx = sin (In²x) + C (A) (B 2 In x In x 2 In x (D

A:

Q: solue the given diffe rential equation by wing The DE IS ho moge hous an appropriale Subrtito tion -...

A:

Q: 2 an is an infinite series with partial sum Sy = 9 – N2 Suppose that n=1 16 What are the values of а...

A:

Q: Aati to determine if the sequence an Use the ratio is strictly increasing or strictly decreasing 6n ...

A: Explained below 

Q: Find the derivative of the function. F(C) = (3t + 18)2/3 f "(t) =

A:

Q: Evaluate the integral using the indicated trigonometric substitution. (Use C for the constant of int...

A:

Q: Verify that the indicated function is an explicit solution of the given differential equation. Assum...

A: We have to verify that y= e-x/3is the solution of differenital equation 3y'+y=0  

Q: The following formula gives the probability of being dealt a full house (three cards of one kind and...

A: topic- permutation and combination

Q: 1. The sum of two numbers is 25. Represent their product as a function of one of them. 2. Monique se...

A: For other questions reupload according to bartleby guidelines

Q: Determine whether the alternating series converges. 7ln k (- 1)*- k k=3 O The series converges. O Th...

A: We have to check weather the given series is convergent or divergent.

Q: Question 3 Find the length of the curve with the given vector equation. r(t) = (8 - 21) i+ (4 + 6t) ...

A:

Q: 3.(Straightforward) Determine if each of these differential equations is exact, and if so, solve it....

A: As per our guidelines we are supposed to answer only one question i.e. the question no 3)a). For the...

Q: Given the graph of the functionf below, evaluate lim f(x). x-00

A:

Q: Find the derivative of the function y = cot^-1 x2 – cos^-1 x + 1/x – 2 %3D

A: To find the derivative of: y=cot-1(2x)-cos-1x+1x-2...(1) Note that: ddx(cot-1x)=-1x2+1ddx(cos-1x)=-1...

Q: 4 du Consider dx. Transforming the integrand, the result will be kJ, where k is a constant. What is ...

A:

Q: F(n) Σ-1)", n3n n=1

A: Question- Determine the radius of convergence of the power series

Q: Given the matrix -2 3 3 6 Find the Characteristic Equation and find its solutions (aka: eigenvalues)...

A: Here we have to find the characteristic equation and eigen values of the given matrix.

Q: Car 1 is heading due south from Math-town at a rate of 40 miles per hour. Car 2 is heading due west ...

A: topic - application of derivatives

Q: Problem 5: Solve the following differential equation for y(t) for the initial value problem using th...

A:

Q: I. Find the derivative of the following functions. 5. f(x) = 5* x5

A:

Q: Find the distance from §= (1,1,5) to the line L: x=1-1, y=2-1, z=31.

A:

Q: The data in the following table shows the outcomes of guilty and not-guilty pleas in 1058 criminal c...

A: topic - prabability

Q: Sec?x Q1) A) Evaluate the following integral: S- V1-tan?x B) Find the slope of the line tangent to t...

A:

Q: • The domain of h is [-3, 3]. h" (x) 0 on -3 < a < -1 or 1 < <3 • There is a local maximum point at...

A:

Q: d) Verify if y = 2e* + x - 1, solves y' = x - y

A: If y=2e-x+x-1, solves y'=x-y