Find the particular solution of the  differential equation with the initial condition given below. dy/dx = 3 - 2x2   ; y = - 2 when x = 0 a. y = 3x - (2/3)x3 + 2 b. y = 3x - (2/3)x3 + 4 c. y = 3x - (2/3)x3 - 4 d. y = 3x - (2/3)x3 - 2

Q: ST/4 x² dx (x²+4)5/2 (Use trigonometric substitution)

A:

Q: 1. Evaluate the following limits. L'Hopital's rule is NOT allowed. 2-√x-1 1. lim 4. lim 5 3x - 4 2.…

A:

Q: 33. (a) L²₁ let - 11 dx r3

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Using trigonometric substitution to solve: sin 2x + C 8 cos x√3-cos²x sin 2x 4 cos x√4-sin²x secx 8…

A:

Q: If f cos*2t dt = At-B sin 2t cos 2t + D sin 4t cos 4t + C where A, B, C and D are constants 24-38…

A: This is a problem related to integration of the trigonometric function. Based on the general formula…

Q: ²1dx = f ( + g(x)) dx, then A + √² g(x) dx is equal to 12. -1 + In(5/2) 1 -1 -1 + In(7) A. B. C. D.

A: The given integral,  ∫x2-1x3+xdx

Q: Question 6 The IBP formula fudv=uv - fvdu can also be written as fudv+fvdu = uv Which of the…

A:

Q: Calculate the derivative. x4-4 y = x²5 (Give an exact answer. Use symbolic notation and fractions…

A:

Q: sin(x)cos(2x)sin(3x) dx A B D sin(3x) cos(3x) sin(2x)cos(2x) sin(2x) + + 12 8 sin(3x)cos(3x) 12 +…

A: We have to find integration of given trigonometric term.

Q: Find polar equation for the Cartesian equation 13y = 8x. a. theta = 1.02 c. theta = 0.55 d. r = 0.55…

A: Substitute x=rcosθ and y=rsinθ in 13y=8x. 13rsinθ=8rcosθ  13sinθ  =  8cosθ

Q: Evaluate the definite integral. Joe²¹i+ i+e¹j+t kdt kat O © 2²² ² x i 2 © (e²-1) e² O e²-1 2 O e²…

A:

Q: e2x+Inx² sin x² dx -+fe²x cos x² dx

A: This is a problem related to integration. Based on the general formula we will solve the problem.

Q: Find the arc length of the parametric curve. L x = 4 cos(t), y = 4 sin(t), z = 3t; 0≤t≤ T

A: Given problem:- Find the arc length of the parametric curve.   x = 4cos(t), y = 4sin(t) , z = 3t ; 0…

Q: Write an equation for the quadratic graphed below: x-intercepts: (-1,0) and (4,0); y-intercept:…

A:

Q: Given the function f(n) = 3n¹ +33n³ +90n²: its f-intercept is its n-intercepts are

A: We can find the intercepts as below in the following steps.

Q: Given: : Saxasin(2x)dx = - ㅠ (A) 3 Зп B 4 c D E 2 3 4 277²-24 64 5T Find bif sbst

A: Let's find.

Q: Given : x³ sin(2x) dx = 277²-24 Find bif sb . 64 2π 3 5π 6 F|+ =|m 3 3π 4 sbst

A:

Q: Find volume of the solid bounded by z = 0, f(x,y) = x² + y², x² + y² = 4², 10y = -6x and 13y = 8x…

A:

Q: dx 1-x² -2

A:

Q: Given: (1+2x) ex dx. Using integration by parts and letting u = − 1 − 2x, dv = f(x)dx, then the…

A:

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A:

Q: Consider using the method of partial fractions to solve x²+x+1 Sa 2x²+2+x²+x A In(x²+1) B x+2 D…

A: This is a problem related to integration of the function using partial fraction decomposition. Based…

Q: 3. Using trigonometric substitution, what is 1 sec-²¹ ( 137 ) + √x²-9 2x² + C A. 1 300² (2) √²-90…

A:

Q: ƒ dx = f(+ g(x)) dx, then A + f g(x) dx is equal to x³+x A. -1 B. -1 + In(5/2) C. 1 D. -1 + In(7)

A: Given that,

Q: (C) EXERCISES Evaluate the following integrals: 1. tan² x dx 2. cot cot² r dr COS I da sin x COST…

A:

Q: Find an equation of the plane containing the point (3,0.-4) and perpendicular to the line r(t)=…

A:

Q: the graph of y = x³ - 6x² + 9x - 2 where the t

A:

Q: Do as indicated. 1 1. Let f(x) = Find the equation of the tangent line to the graph of f'(x) at the…

A:

Q: Sa 2x²+2+x³+x² =dx = [Aƒ (x) — B ln(g(x)] + D fb dx, and if A = ,B<0, then f(x) dx x+2 x² 2x + + 5…

A:

Q: what is the normal equation to the curve which is the circle with center at origin and and radius of…

A: Given circle , With center at origin (0,0) And a point on circle is (4,3)

Q: Use geometry to evaluate f(2x+5)dx

A:

Q: B C D N Given: √-x² + 4x+5 dx. Using trigonometric substitution, what is the integral form in terms…

A:

Q: For the function f(x) given below, evaluate lim f(x) and lim f(x). X18 8118 -x³ + x f(x) = √4x6 - 3…

A: We can solve this as follows:

Q: Question 8 Using trigonometric substitution, what is f √x²_9 x3 A sec (-²) – + C √x²-9 6x² B √x²_9…

A:

Q: Determine the open intervals on which the graph of = 3x² +7x - 2 is concave up or concave down.…

A:

Q: y=x√1 + x²

A:

Q: Let (A) = and B D= . 04 O -2 02 none of the above Find (A) 0.BO*

A: Given  problem:- (A) = &lt;1, 2,3,4&gt; , (B) = &lt;0, -1, 4,-2&gt; Find (A). (B)

Q: 15x²x³43x - 19 The integral (x + 1)²(x² - 6x +13) Ax + B What is the value of x²+bx+ca -dx? 3 A…

A: This is a problem related to integration. Based on the concept of partial fraction decomposition we…

Q: Given the function C(a) = (x-4) (x + 6) (x - 1) its C-intercept is its x-intercepts are

A: Solution is given below:

Q: Find the total area bounded by the x-axis and the curve y = f(x) on the indicated interval. f(x) =…

A:

Q: 1 x√x²-2x =dx : √x²-2x x =+c C

A:

Q: A group consists of four men and seven women. Six people are selected to attend a conference a. In…

A:

Q: How many different 5-digit phone numbers do not contain the digit 6? Assume that any digit in the…

A:

Q: c. The region R enclosed by the curves y = x and y = x² is rotated about the line y = 2. Find the…

A: Using disc method, volume of solid is evaluated.

Q: Linearly dependent solutions Undamped Free vibrations w=0 W=W₁ (undamped) Principle of Superposition…

A: Given:-

Q: dx 1+tan x

A:

Q: dx Arcsin (²) + c

A:

Q: Find the derivatives of the function xy² x-y x + y

A:

Q: Suppose that $2000 is placed in a savings account at an annual rate of 4.2%, compounded monthly.…

A:

Q: 4d³y-13 +6y=0 dy dx3 dx

A: