Q2) Find the area of the surface generated by revolving the curve y=√4-x² about y-axis.

Q: Let f(x, y) = ln(x + y − 1). Then, ƒ(1, 1) =

A: The given function is;  f(x,y)=ln(x+y-1).

Q: Evaluate the given integral by changing to polar coordinates. sin(x² + y²) da, where R is the region…

A: Given :∫∫Rsinx2+y2dAR :Radius of unit circle is 3 and 4

Q: The approximated value of the integral fe* dx is equal to - Rule with step size (h=2). when using…

A:

Q: J sin(lnx) dx

A: Let's solve given integration.

Q: In problems 1 and 2, list both the order of the DE and state whether the DE is linear of nonlinear.…

A:

Q: Determine the slope of the tangent line to the curve y=2 – x2 at the point (3,-7)

A: slope of tangent = slope of given curve  step 1  we have to find slope of curve  slope = dy/dx  so…

Q: An object is dropped from 260 ft. above the surface of the moon with an initial velocity of 0…

A: Let's solve for time taken the object to hit the surface of the moon.

Q: Sketch left-endpoint and right-endpoint approximations for f(x) = on [1,2]; Approximate the area…

A: fx=1x on 1,2, n=4

Q: Find the general solution of the following DE. y' = 3 (y + 1) O y = 3ce³x - 1 Oy = ce³x - 1 Oy =…

A: y' = 3(y+1) dy/dx = 3(y+1) dy/3(y+1) = dx dy/(y+1) = 3dx now apply both side integration

Q: 12. Integral x² dx x³ +4

A: Given the integral,        ∫x2 dxx3+4

Q: A box with an open top is to be constructed from a square piece of cardboard, 3 ft wide, by cutting…

A:

Q: Assume that the situation can be expressed as a linear cost function. Find the cost function. Fixed…

A:

Q: 3 fx²³√₁² + x² dx X 2 a

A: Sol

Q: Calculate the future value of end- of-month payments of $500 made for 4 years into an investment…

A:

Q: Q1.B. if k-1 is an eigen value of (₁2). find one corresponding eigen vector?

A:

Q: Use differentials to estimate the amount of paint needed (in m3) to apply a coat of paint 0.04 cm…

A: Our Aim is to find the amount of paint required to coat thickness of 0.04 cmby considering a…

Q: and a) x = y² + 1₁ x = 0, y =- y = 2 The volume generated by revolving the region about the line y=2…

A: We can solve as follows

Q: 8. Let R be the region bounded by y = √25-2² and y = 3. Find the volume of the solid generated when…

A: I have stated the used formula in the solution.

Q: Evaluate √t (3t-t²) dt

A:

Q: (y − √√x² + y²) dx − xdy = 0 when x = x √(x² + y²) = 1 Option 1 y-√√(x² + y²) = 1 Option 3 y —…

A:

Q: 1 3x (2x + = + ₁). x+1 Find k'(x) if k(x) = 3x (2x + Provide your answer below: k'(x) =

A:

Q: Find the general term of the sequence, starting with n = 1. Determine whether the sequence…

A: A Sequence is said to be convergent if it approaches some limit. A sequence is said to be divergent…

Q: Evaluate the following double integral by converting to polar coordinates where J 5xy 2x² + 2y² R…

A:

Q: solve the system of equations by Grammer Method. 3x₁ −2x₂ + 4x3 = 19 x₁ +5x₂ −x3 = -12 2 x₁ + 2x₂ +…

A:

Q: 5. Iny+ea²²x+y = 10 -

A: Given :According to given , only 5 solvedlny+ex2y2-x+y=10

Q: 1. a- Find a result by using variable separation for dy dx b- y³y+x³=0

A: Note:- These are multiple questions and acording to our company guideline we can do maximum 1…

Q: Find the derivative of f(x) = (-x³ - 2x² - 2x) sin (x). Do not include "f'(x) =" in your answer.…

A: Topic = Derivative

Q: Given the functions: f(x) = x³ - 2x g(x) = √2x h(x)=2x-1 Evaluate the function (gof)(x) for x = -3.…

A:

Q: The pressure P and volume V of an expanding gas are related by the formula PVb = C, where b and C…

A:

Q: Find the integral of the following indefinite integral equations: Jx dx / (5 + 9x4) Jx dx/v(16-9x4

A:

Q: Find the average value of: f(x) = 8 sin x + 3 cos x on the interval [0,1] 3 Average value =

A: Solved below.

Q: 1. Find the solution of the following differential equation? Then find the particular solution with…

A:

Q: Determine the modulus and the principle argument of the following complex number: (2 + 4i) (2 + 2i)…

A:

Q: Find the volume, in cubic units, generated by revolving about the x-axis the area bounded by the…

A: Solution is given below:

Q: Question 1. A critical point of the function g(x, y) = ey + 3x²y-y is (0,0). Use the Second…

A: See this solution in below

Q: Evaluate the following antiderivatives. 2dx x ln x S

A:

Q: S x² e¹x dx

A: EVALUATE USING INTEGRATION BY PARTS  For the function x2e4x .

Q: 5. Test the ff ODE for exactness and find the general solution of the DE (2x + 3y) dx + (3x + 4y)…

A: To solve Differential equation.

Q: Using the two points (x,y) and (x₁,51) to find Lagrange interpolating polynomial, L.(x1) is always…

A:

Q: I. Integration by Parts. Evaluate the following integrals. 3. sin (In x)dr

A:

Q: For the function f(x) = 7x³ − 2x² + 2x + 9, find f''(x). Then find f''(0) and f’’(9). f''(x)= Select…

A: Derivatives

Q: ³ sin y - 3) = √10 ² Let f(x, y) dt 1 + cos² (t) 16 Then f (2, π/6)=

A:

Q: 6. Integral Df ef

A:

Q: Use the method of reduction of order to find a second solution of the differential equation t²y" —…

A:

Q: Find the derivative of f(x) = (-x³ - 2x² - 2x) sin(x). Do not include "f'(x) =" in your answer.…

A: Topic = Derivative

Q: 2. Find x (round your answer to 2 decimal places) 80° 70° 7 X

A:

Q: Find the largest open interval where the function is changing as requested. 24) Increasing…

A:

Q: 4. Solve the following DE using a suitable type of transformation. y' = x + y (let v = x + y) O y =…

A:

Q: 89% of 35

A:

Q: Let k(x)=f(x)g(x)h(x). If f(−2)=−5,f′(−2)=9,g(−2)=−7,g′(−2)=8,h(−2)=3, and h′(−2)=−10 what is…

A: