Product/Quotient/Chain Rules for Differentiation: Answer the following

Q: Find the area of the region bounded by y = (1/8)(-x² + 6x +7) and y = -6. Answer:

A:

Q: The general solution of the differential equation dy/dx 12x is y = 4x + C. Select one: O True O…

A: A separable differential equation can be written is of the form of dydx=f(x)g(y).

Q: EVALUATE EACH OF THE FOLLOWING INDEFINITE INTEGRALS. Show step by step solution . 1.

A:

Q: Find V. (V x F), if F(x, y, z) = 7e**i+ 8xej – 3elk.

A:

Q: (x+ct u(x,t) f(x- ct) +f(x+ ct)] + g(y)dy x-ct

A: solution

Q: A population of 200 kangaroo is released into the forest. During the first three years, the…

A:

Q: Distinct Real Roots of Auxiliary Equation the general solution (D² – 9)y = 0 (D² – 1)y = 0 -

A: Topic:- solution of differential equation

Q: Q(t) = Q0: 2-(t/140) If the amount of polonium left after 560 days is 80 mg, what was the initial…

A:

Q: Find the indefinite integral. (Use c for the constant of integration.) (4t³i + 12tj – 8Vik) dt Need…

A:

Q: A general solution of the differential equation - 3+4 = 0 is 1. A. y = c,e* +cze2x + c3xe²x B. y =…

A:

Q: 1. S sin x cos 3x dx.

A:

Q: One of the correct steps to evaluate x2Inx dx to yield the correct integral

A: Our Aim is to identify the correct step to evaluate ∫x2 ln (x) dx to yieldthe correct integral.

Q: 1) Use a double integral to find the area of the region enclosed by y= x² and y = 2x.

A:

Q: Find V · (V × F) if F(x, y, z) = 3 sin xi + 9 cos(5x – 6y)j+ 10zk.

A:

Q: r arcsin(5y) dy. Consider the integral V1– 25y? This can be transformed into a basic integral by…

A:

Q: At the beginning, an experiment records 1 gram of bacterial culture, and the culture's weight is…

A: we have to find weight at t=10 hr.

Q: 1. Find the area bounded by the parabola y?=4ax, the x-axis, and the lines x=4a, x=9a. 2. Find the…

A:

Q: The particular solution that satisfies the differential equation and the initial condition of dy/dx…

A:

Q: 4.) on this item Pinal (Vx+Vx)* dx Use only The Method of substitution/u-substitution answer should…

A: We have to find the integral

Q: Write a definite integral that represents the area of the region. (Do not evaluate the integral.) Y1…

A:

Q: Write and evaluate the definite integral that represents the volume of the solid formed by revolving…

A: We need to find volume.

Q: A projectile fired downward from a height of 112 ft reaches the ground 2 seconds. What is the…

A:

Q: Which integral corresponds to the volume of the solid generated by revolving the region enclosed by…

A:

Q: S- dx x?V4-x?

A:

Q: 1. Find the area of parabola y = x² from 0 to 1.

A: This is a problem related to integration. Based on the integral formula for area calculating we will…

Q: function f has the following graph: 4- 3 2 1. -1 6 7. 8 -1 -2 Vhich of the following is true? O The…

A: Given query is to find the correct statement for the function.

Q: dy (х — 1) — у + 2(х — 1)3 dx

A:

Q: dx tan x +sin x+1

A: Solution of the problem as follows

Q: Find the general solution of the following: 1. (4D2 – 4D + 1)y = 0 %3|

A:

Q: Find the area of the plane region bounded by y = x3, x = -2 and x = 2.

A:

Q: x = 3 sin? (2t) – 2 ;teR y =1-3 cos (2t)

A:

Q: Find r'(t), r"(t), r'(t) - r"(t), and r'(t) x r"(t). r(t) = 2t2i – 3tj + t3k (a) r'(t) (b) r"(t) (c)…

A: To find r'(t), r"(t), r'(t).r"(t), r'(t)×r"(t).

Q: Find the value of n in the following definite integral. S“ 4x*dx = 1

A:

Q: Find the derivative of y=x^(7sinx). (x>0).

A:

Q: dy Find for dx 4) y= sinxtanx

A:

Q: Which integral corresponds to the area of the shaded region between the curves y = -x? + 3x and y =…

A:

Q: Solve the logarithmic equation algebraically. Approximate the result to three decimal places. (If…

A:

Q: Solve the De as follows via Laplace transformations: y"- (14/3)y" - (55/3)y' + 14y = 0; y(0) = -1,…

A:

Q: Find the area of the plane region bounded byy x, x = -2 and x = 2. Answer:

A:

Q: y" + y' – 2y = 2t, y(0) = 0, y'(0) = 1

A:

Q: 20 u(x) = 0.3e(0.5(-x+ 275.1)) + 3.62 21 v(x) = -1.2 log, (0.3(x – 269.73))+4.4

A: We need to find derivative.

Q: 8 – a? if – 2 2 between O 8 and 16 O O and 8 O 16 and 24 O 16 and 33

A: Given problem:-

Q: 8. A lamina occupies the top half of the disk x² +y? <4. The density at any point on the lamina is…

A:

Q: dy Find for dx 5) y = sec-(2e3x)

A:

Q: How many arbitrary constants will be there n the general solution of a second order differential…

A: The number of arbitrary constants in the general solution of a differential equation is equal to the…

Q: Find two values of 0, 0so<2n, that satisfy the following equation. cos = 2 (Simplify your answer.…

A:

Q: Find an equation of the largest sphere contained in the cube determined by the planes a 1, a = 7, y…

A:

Q: ||F(t) × r"(t)|| ||r(t)||* Use the formula k(t) = to find k(t). r(t) = e""i+e-tj K(t)

A: To find out the k(t).

Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. y = -x2 -…

A:

Q: The position vector r describes the path of an object moving in space. Find the velocity v(t), speed…

A: