Let the region R be the area enclosed by the function f (x) = e® + 2 and g(x) = 6x + 3. Write an integral in terms of x and also an integral in terms of y that would represent the area of the region R. If necessary, round limit values to the %3D nearest thousandth. 22 21 20 19 18 17 16 15 14 13 12 11 10 9. 2 X2 = dx Y2 dy Y1

Q: Use Lagrange multipliers to find the minimum distance from the curve or surface to the indicated poi…

A:

Q: Given f(a) = 1- 홀 (3 + 4a) + 용(3+ 4z)2 - 꿈 (3+ 42)3 then f'(x) = 27 (3 + 4x) 8. 흥(3+ 4z) + (3+ 4z)2…

A: topic - derivative of a function

Q: estion Evaluate:S sin (3x) cos³(3x) dx r answer estion Ising Trigonometric Substitution, evaluate: -…

A: Solution:

Q: x² – 16 Evaluate lim x4 2- Vx O -32 None of these 1 O 32 O does not exist

A: Given  Lt   x²-16/(2- √x)        x->4

Q: What is the value of csc(0) if the terminal side of the angle 0 intersects a circle at the point…

A: At first we want to find radius of the circle.

Q: a) Find the degree 3 Taylor polynomial T3 (2) for the function f(x) = 4 cos(r) centered at the point…

A: The function f(x)=4cos(x) centered at the point a=π4

Q: Find Ay and f'(x)Ax for y = f(x) = 6x, x =4, and Ax = 0.06.

A:

Q: Find the equation of the tangent line and the normal line of the curves at given point 1. y = x V16…

A: Equation of tangent line Consider y=x16+x2slope of the tangent line is dydx  at…

Q: EXERCISES write the number in the form a + jb. (a) – 31 (b) (8 + j) – (5 +i)

A:

Q: Question 7 Given f"(x) = 2z – 6 and f'(- 2) = – 4 and f( - 2) = 2. Find f'(x) = and find f(4)…

A: Given query is to integrate and find the function.

Q: Determine whether each point lies on the line. x = -2 + t, y = 4t, z = 5 + t (a) (0, 8, 7) O Yes No…

A: topic - lines and points

Q: dy J 1+y+1

A:

Q: Give the augmented matrix for the following system of linear equations. -3x1+10x2-6x3-4x4+8x5 = -4…

A:

Q: dy = (Type an integer or a simplified fraction.)

A: Topic:- double integration

Q: Find the gradient of the function at the given point. f(x, y) = 2x + 5y2 + 10, (3, 4) Vf(3, 4) еBook

A:

Q: dx x'+3 Xん X

A: We have to solve the integral.

Q: hFind the gradient of the function at the given point. W = x tan(y + z), (19, 4, –1) Vw(19, 4, –1) =

A:

Q: Learning Task 3: Identify whether the given graph illustrates an extreme value theorem or not.…

A:

Q: What is the reference angle of O if 0= -137°? A 43° B 47° C 137° D 223°

A: Given query is to find references angle.

Q: lim f(x) = c lim f(x) = 00 lim f(x) = 0+ lim f(x) = 0- x-1+ X-1- f(0) = 0,f(-1) = -f(-2) = -

A:

Q: Solve the initial value problem. dv 8 t> 1, v(2) = 0 dt

A:

Q: A box is to be constructed from a piece of square cardboard whose perimeter is 36 inches by cutting…

A:

Q: At which points on the curve y = 1 +°40x³ – 3x³ does the tangent line have the largest slope? | (x,…

A: Maximize slope

Q: Consider the function y = 4ex + 7. What is the exact value of C in the interval [0, 5] such that…

A: We need to find value of C.

Q: A rectangular lot having an area of 5000 sq. meters is to be fenced on three sides. Find the minimum…

A: topic - application of derivatives

Q: Recall: v = can be written as v = ai + bj + ck , where i = , j = and j: . Let v = – 2i + 5j – 4k…

A:

Q: The edge of a cube is changing at the rate of 0.2 cm/sec. How fast is the volume of a cube changing…

A:

Q: 6. Determine, with reasons, the absolute maximum and absolute minimum of f(x) = x/2 – x on the…

A:

Q: 1+cos4x 1. 1-cos4x -csc2xdx

A:

Q: The sum of two numbers is 8. The product of the first number and the square of the second number is…

A:

Q: af Given f(x, y) = In(6x² + 8y²) then %3D

A:

Q: Find the dimensions of a rectangle with area 216 m2 whose perimeter is as small as possible. (If…

A:

Q: 2xydx+(x^2)dy=0

A:

Q: Find Sc F · dr for F = 3yi – (sin y)j on the curve counterclockwise around the unit circle C…

A:

Q: Find the absolute maximum and absolute minimum of the function on the interval. f (x) = 5(x² -4)/z³,…

A:

Q: dx U x" Jx? +3 4

A: To find out the integration.

Q: 1. The Fibonacci sequence is given by the recurrence relation a, = a,-1 + a,-2; a, = 0, a, =1. Write…

A:

Q: V3 - 2s ds 02 40

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Let S denote the cone x? + 4y? = z². (a) Find an equation for the plane tangent to S at the point…

A:

Q: 2- -1- -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 3 -1 -2 -3 --4 -5 -6 -7- Provide your answer below: lim f(x)…

A:

Q: Find the dimensions of a rectangle with area 216 m² whose perimeter is as small as possible. (If…

A: Find your answer below

Q: 1 a. f(x)3D 4 b. g(x) = - X c. h(x) = 3 -

A:

Q: Question Using Trigonometric Substitution, evaluate: S e4*/1+ e2xdx Your answer

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Find parametric equations of the line through (-1,0,1) that is parallel to 2i – 6 j+ k. -

A:

Q: 4. [V40-4v-v² dv

A:

Q: Find the directional derivative of the function at P in the direction of v. f(x, y, z) = xy + yz +…

A:

Q: y' + 3xeY = 0

A:

Q: Find the dot product of the following vectors u and v. %3D

A:

Q: Find Ay and f'(x)Ax for y = f(x) = 6x°, x = 4, and Ax = 0.06. Ay = (Round to four decimal places as…

A:

Q: Find the gradient of the function at the given point. In(x2 - у) - 3, (2, э) Vz(2, 3) = %3D

A: