Set up the equation in solving volume of the solid generated when the area bounded by a = √√√y, x = 0, and y = 3 with the axis of revolution at y-axis using horizontal strip. 132 OV= (2²) ² dy OV = f (√)² dx OV=(√)² dy

Q: For a given cylindrical tank, the radius is 2m and the height is 18m. The tank is filled to a depth…

A:

Q: Evaluate the integral by interpreting it in terms of areas. In other words, draw a picture of the…

A: Given problem:-

Q: Write the form of the partial fraction decomposition of the rational expression. DO NOT find the…

A:

Q: 1. Find the domain of the vector function r(t) =< ln(t + 2), t 1 - 12 21 √12 - 4

A:

Q: nd the general solution to the differential equation ut the problem in standard form. nd the…

A:

Q: Use the gradient to find the directional derivative of the function at P in the direction of PQ.…

A: Given that, the function is gx,y,z=xye8z and the points are P3,12,0 and Q0,0,0.…

Q: Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of…

A:

Q: 3) [ Consider the DE: -(4x³y - 16)dy = (6x²y² - 10)dx. A) Show that the differential equation is…

A: Given :-4x3y-16dy=6x2y2-10dx

Q: Determine whether The given series M8 k=2 ខណៈ k=2 1 √k-1 1 √k-1 converges using the Comparison Test…

A:

Q: Suppose that f is a differentiable function with f(2) = 5. If the tangent line to the graph of y =…

A:

Q: The function f gives the weekly profit, in thousand dollars, that an airline makes on its flights…

A:

Q: Find the limit of the following sequence or determine that the sequence diverges. 2n² 1 6n² + 1 -…

A: Solve the following

Q: Given: In (sin² 3t) = e = arc cot (w) Find: dw dt O(1+w²) (6cot (36) e) [ Oet+w²et - 6tan (3t) - 6w²…

A:

Q: Use the given information to find the exact value of the trigonometric function.  sin θ = 1/4 , θ…

A:

Q: F. (DERIVATIVES OF EXPONENTIAL AND LOGARITHMIC FUNCTIONS) 1. Find f'(x) if f(x) = 3e². 2. Find g'(x)…

A:

Q: x - 1 = λχ y = 2 = λy z = -λz (x² + y² = z² = 0,

A:

Q: dy Find using implicit differentiation. dx Hint: First clear the denominator to get 8x² + 6y =…

A:

Q: Find the interest earned on $30,000 deposited into an account paying 2.5%. Round to the nearest…

A:

Q: Set up the definite integral required to find the area of the region between the graph of y = 13-²…

A:

Q: A man of height 1.9 meters walks away from a 5-meter lamppost at a speed of 1.1 m/s. Find the rate…

A: topic- application of derivatives

Q: Sy²sin (2y) dy

A: Integration by parts.

Q: Given that the graph of f(x) passes through the point (5,10)( and that the slope of its tangent line…

A: Given , The graph of f(x) passes through the point (5,10) and that the slope of its tangent line at…

Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 by the vectors u, v and w…

A: Solution is given below:

Q: The limit: exists, and equal to 0 Select one: True lim (x,y)-(0,0) Falas x-y x² + y² The gradient…

A: Here we have to check whether the statement is true or false.

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of PQ.…

A: Here we have to find the directional derivative.

Q: Integrate O √25 - 2² 2 ▶ X 25 - x² O. + C V6-ਏ 25 - x² 2 dx. +C 25 - x² + C 25 - x² + C

A: topic- indefinite integral ∫xn dx=xn+1n+1+C

Q: C What is f" (x) of f(x) = x Arc sin(x) + √1 − x²? Arc sin(x) 2 √1-2² √1-7² ◄ Previous + Arc sin(x)

A:

Q: A man has 27 coins in his pocket, all of which are dimes and quarters. If the total value of his…

A: A man has 27 coins in his pocket, all of which are dimes and quarters. If the total value of his…

Q: Find the normal vector to the level curve f(x, y) = c at P. f(x, y) = 6 - 4x - 7y c = 6, P(0, 0)

A:

Q: The curve y = ax³ + bx² + cx + d has a critical point at (-1,3) and has a point of inflection at…

A: We are asked to which is true for the given condition  Note: Critical points are points where the…

Q: Use the given information to find the exact value of the trigonometric function.  cos θ = 4/5 , θ…

A:

Q: Workout Problem j Part a: ( 1. Find the domain of the vector function r(t) =

A:

Q: The partial derivative fx(-1,0) of ƒ(x, y) = xe³ + x² + 1 is equal to −1. Select one: True False

A:

Q: O ди If u = f(x,y), x = g(w) and y = h(w), using Chain Rule, what is aw O ди aw ди Əw || O all of…

A: u=fx,y, x=gw and y=hw

Q: Which of the rectangles below are both left and right rectangles? 10- 8- 6- 4- 2- 0- 0 8 CD 0000 05…

A: Rectangle which is both left and right rectangle is the rectangle which touches the function from…

Q: 15 0 2) is an eigenvector of the matrix 25 -12 -6 A = 60 -31 -15 -36 22 10 associated with the…

A:

Q: u⃗=5i⃗−j⃗− k; v⃗=−i⃗+5j⃗+8k.  Find the projection of u ⃗ onto v :⃗

A:

Q: Write the first five terms of the geometric sequence. a 1 =  -5; r = -3

A: We can find the first five terms as below.

Q: Part b: (**) We consider the function f(x, y) = x sin y - y cos x + X-R y Find fx(x, y), fxy(x, y),…

A:

Q: Let f(x, y) = domain of f is the set D = {(x, y)|x² + y² > 1}. Select one: 1 1 - x² - y² True O…

A: Given.

Q: The number of oil changes per hour at Quick Lube is described by the following short-term production…

A: answer is in next step .

Q: Sketch the region enclosed by y = 3x and Y = find the area of the region. 2x². Decide whether to…

A: Given that y=3x and y=2x2To find : Area between the region.Solution :

Q: Consider the following. lim (1+1)* X-00 (a) Describe the type of indeterminate form (if any) that is…

A:

Q: Consider - 2x 2) (² f(x, y) = e fxx + fyy = 0 cos 2y - e -2y cos 2x. Verify that

A:

Q: A bush fire is burning a circular area whose radius is increasing at a rate of 3 ft/min. How fast is…

A:

Q: 4 (a² - y²)² 4. g(x) = (3x² + 4x - 5)5 3. 2 =

A:

Q: Solve the following triangle. B = 70°, C = 50°, b = 8 O A (Simplify your answer.) a≈ (Type an…

A: We will use law of sines to solve this question.

Q: Integrate I -dz Select one: O A In 1-¹-2²+√1 − x² + C I OB. 21n1-¹³+√1 − x² + C | OC. In 1-²+√1 = z²…

A:

Q: Find the limit of the following sequence or determine that the sequence diverges. {tan - 1 (₁ -1…

A: Here we have to find the limit of a sequence.

Q: Use the Integral Test to determine whether the following series converges after showing that the…

A: If f(x)  is a continuous, positive and decreasing function on the interval [k,∞)  and  f(n)=an…