Find the volume of the region in the first octant bounded by the coordinate planes, the plane x+y=5, and the cylinder y^(2)+z^(2)=25.

Q: Solve the given initial-value problem. Y(x) = y" + 4y' + 5y = 35e-4x, y(0) = -5, y'(0) = 1

A: y'(0)=1

Q: 4. Use Calculus to graph g(x)=x² + 4x³. Make sure that your graph shows all intercepts, extrema, and…

A:

Q: 2) Find the solution of the given initial value problem in explicit form. Plot the graph of the…

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: r(t) = 2t²1 - 4tj + 2t³k (a) r(t) (b) r"(t) (c) r(t)r"(t) (d) r(t) x r"(t)

A:

Q: 10 P.M. an oil tanker traveling west in the ocean at 15 kilometers per hour passes the same spot as…

A:

Q: Find the area of the region enclosed by y=4.75x and x = 9 - y². 2 on 5 6 7 00 a Use horizontal…

A:

Q: 1. Using the fundamental theorem of calculus part 1, along with properties of the definite integral…

A:

Q: lim √xe-x/2 x → 00

A: L=limx→∞xe−x/2

Q: Recall that a sequence is a list of numbers while a series is a summation of numbers. 1. Let an = n…

A:

Q: What is the volume if a 6 inch square is cut out

A: Consider the box

Q: What is the center of the sphere given by the equation x² - · 6x + y² – 2y + z² +82 +17 = 0? -…

A: The standard equation of a sphere is given by  where (h,k,l) is the center of the sphere and r is…

Q: Solve the second order. Dieg - Ý - ý syes 1 39

A:

Q: Consider the function f(x, y) = x²y+y³ — 27y. f has f has a maximum a minimum f has a saddle f has…

A:

Q: Express 0.132 as a geometric series

A: The given number .The aim is to write the number as a geometric series.

Q: (1) (2 cos y + 4x²)dx = xsin ydy

A: given differential equation

Q: Evaluate the following limit. lim 8+←8 15 ln x X = Note: Input DNE, infinity, and -infinity for does…

A: Given,

Q: Use Rolle's Theorem and a proof by contradiction to show that the function f(x) = 6x³ + 4x - 11 does…

A:

Q: Consider the following. Find y'(x). y'(x) = y = X = X x² +9 Find the critical numbers of y(x).…

A:

Q: If what are the bounds of integration for the first integral? a= 11 [ f(a)d= = [ f(x) dx + " f dx […

A:

Q: - Consider the function ƒ(x) = x² − 4x + 2 on the interval [0, 4].

A: f(x)=x2−4x+2 on the interval [0,4]

Q: The graph off consists of line segments, as shown in the figure. Evaluate the definite integral 11…

A:

Q: ²-3x. If there is more than one, separate with a comma.

A:

Q: Find dy/dx and d'y/dx, and find the slope and concavity (if possible) at the given value of the…

A: The given parametric equations

Q: 2. Determine whether the series n Σ» (-1) (3) converges or diverges. If it converges, find the sum.

A: The given series is

Q: Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method,…

A:

Q: If 1800 square centimeters of material is available to make a box with a square base and an open…

A: Let the side of the square base = x cmLet height of box = y cm

Q: Q/ solve equations 1- y' = ky 2-x(1+y²) dx =y(1+x²) d;

A:

Q: Consider g(t) = 3t+ 6t² - 1 + 6t³+2+¹ Determine the intervals on which g is concave down. g is…

A:

Q: Find a Cartesian equation for the curve. r = 9 cos(0)

A:

Q: Give the partial fraction decomposition for the following expression. x² - 6x +29 2 X (x - 5)(x-1)(x…

A: we need to give partial fraction of

Q: Find a Cartesian equation for the curve. r = 5 sec (0) 2π X

A:

Q: 4. COS V sin v = csc v sin v 5. cot(a) cos(-a) + sin(- α) - csc (α)

A:

Q: Solve 12 4x+1 <3

A:

Q: Given that f(x)= Only one item from the answer bank will be used to complete each category. Not all…

A:

Q: A point is moving along the graph of the given function at the rate dx/dt. Find dy/dt for the given…

A:

Q: 9. Locate all relative maxima, relative minima, and saddle points of the fol- lowing function f(x,…

A: The given function is

Q: Find the absolute maximum and absolute minimum values of f on the given interval. π [7] 0, 2 f(t)= 2…

A: In this question, we will find the absolute maximum and minimum values.

Q: List the first five terms of the sequence. an 1 + an a1 a2 аз a4 a5 || = = = a₁ = 6₁ an+1 =

A:

Q: Suppose that lim f(x) = 6 x 3 and lim g(x) = 8 x-3 Enter the exact value of lim (fg)(x) 2-3

A: Suppose that .To find the exact value of .

Q: 6. Let f(x, y) = sin(x + y). Answer the following questions. (a) ) Find the gradient f(x, y). (b)…

A:

Q: Consider the function graphed to the right. Make sure to use the union symbol, U if needed. The…

A:

Q: 2. Isolatex. For answer, show this structure <x< -5 ≤ 2-x < 5

A:

Q: Let h(x) = 6x² +1+17x Determine the critical values of h. If multiple such values exist, enter the…

A: Given, .For find critical valuer put h'(x)=0.

Q: Find the absolute maximum and absolute minimum of the following function on the given interval. 1…

A:

Q: (b) Isolate дет 11 2x 5 = 1/2gt²2² + vt

A: To isolate  in the following equation.

Q: Find all critical numbers c of f(t) = 3t²/³ +t5/³.

A: f(t)=3t2/3+t5/3

Q: Tel f(x) = at: *+] at x = 2

A: The given function is

Q: Evaluate the following integral 6x + SS (8x - y) In (8x - y) dA R where R is the region bounded by…

A: Given that, where R is the region bounded by the graphs of                  Using the change of…

Q: An = (3″ + 5n)1/n

A:

Q: describe what you would have to do to your graph of f(x) to sketch g(x)= (x+1)^2-4(x+1)+3

A: The given function is .The aim is to describe how to sketch the graph of the function using the…