Find the exact area of the surface obtained by rotating the curve about the x-axis. y = √ 1 + ex, 0≤x≤4

Q: At which octant will you find (-8, 13, -1/2)?

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Q: (5+162²) ²- Question 16 Find the curvature of the plane curve y = 5x² +8 at x = -1. Round your…

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Q: given u= and v= find uXv

A: To solve the following problem

Q: Find the volume of a sphere pyramid of height "h" and base edge of length "a"

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Q: Use a graphing calculator to determine which expression can be used to complete the identity below.…

A: topic- trigonometric identities identities useda3+b3=(a+b)(a2+b2-ab)sin2x+cos2x=1

Q: Find the partial derivative fx for the function f(x,y)=√16x+y³ |f₂(x, y) = O f.(x,y)= f₂(x, y) = 1…

A: We have to find derivative

Q: 3. What are the values of A, B, and C so that a. A = -2, B = 3, and C = 4 b. A = 2, B = 3, and C= -4…

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Q: What is the y-coordinate of the y-intercept of the secant line of the square root function at x=1…

A: Here we have to find the y-intercept of the secant line

Q: Rationalize the numerator. 2-2 sin y 2 + 2 sin y 2-2 sin y 2+2 sin y (Simplify your answer.)

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Q: Evaluate INIM -6 x³ dx √x²-9

A: To find out the definite integral.

Q: Calculate the sum of the series Σ n = 5-6(0.6)" 00 n = 1 n whose partial sums are given.

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Q: Calculate the double integral. 7x S₂ x ² + x²0² +y dA, R= [1, 4] x [0, 1]

A: Explained below

Q: Suppose S. f(x) dx = 36, [₁² f(x)dx = 12, ²9(1 1. (2f(x) + +12g(x) — 4h(x)) dr g(x)dx = 24, and h(x)…

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Q: 1. Use the fact that coshx = (e* + e) and sinhx = 1 NIH (ex - e-*) to solve for 1 coshx+ sinhx dx

A: ∫exdx=ex+c

Q: Use Taylor's Inequality to estimate the accuracy of the approximation f(x) ≈ T₁(x) when x lies in…

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Q: 2. A function is said to be if, graphically speaking, you can trace the entire curve without any…

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Q: Find the derivative of the function f(x) = (5x^4)/12

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Q: lim X-00 X *3)* X 1 1+

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Q: w = sqrt(25-4x2- 4y2) ,  x=r cos(theta) ,  y=r sin(theta) (b) Find del w / del r and del w / del ?…

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Q: 7x (x+3)³ a. Find lim F(x). X-3 Let F(x)= b. Find the vertical asymptote of the graph of F(x). c.…

A: F(x)= 7x/(x+3)3  a) find the limit of F(x) when x tends to -3 .  b) find the vertical asymptote of…

Q: + 2x)² 4x +2

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Q: Evaluate the double integral. Sxy² da, D is enclosed by x = 0 and x =

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Q: The mess in a house can be measured by M(t). Assume that at M(0) : = 0, the house starts out clean.…

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Q: Find all relative extrema. Use the Second Derivative Test where applicable. (If an answer does not…

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Q: Find the principle unit normal vector to the curve given below at the specified point. r(t) = ti+…

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Q: 6. Σ(-1)n-1 sin (2) n=1

A: Explanation of the answer is as follows

Q: Find the critical numbers of f (if any). Find the open intervals on which the function is increasing…

A: We have to find the critical numbers of the given function. Also, we have to find the intervals on…

Q: QUESTION 5 Find the 2nd solution by reduction of order. y" - 4y +4y=0; y₁ = e²x

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Q: Find the total differential. z = ex tan(y)

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Q: Find the first partial derivatives with respect to x, y, and z. 3xz x+y aw əx Əw ?у Əw əz || W = (No…

A: This question can be solved using the concept of partial derivatives.

Q: and & and ß are between 0 and f/2. 3

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Q: The figure to the right shows four regions bounded by the graph of y=xsin x: R₁, R₂, R3, and R4,…

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Q: What is the general solution to y² tan(x) dy = sin(x) dx o y = √3 sin(x) + C o y = -√√3 cos(x) + C o…

A: Here we have to solve the differential equation.

Q: S." (inx+4)" x dx

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Q: 2. Use integration by parts to solve for [x³c x³ cosx dx.

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Q: find the area of parallelogram A=(0,2,0) B=(2,5,2) C=(3,8,4) D=(1,5,2) round to 2…

A: The given points are A=(0,2,0), B=(2,5,2), C=(3,8,4), D=(1,5,2)

Q: Show your complete solution: Evaluate the triple integral ㅠ pxy 2 L x 0 COS Zdzdydx X

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Q: Question 12 a)! Let C be a curve defined by the vector equation r(t)=. P(32, 52, e³2) Show that the…

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Q: A store finds that its sales revenue changes at a rate given by S'(t) = -30t² + 400t dollars per day…

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Q: Given that S." sin xdx = 2, find the average value of the sine function on the interval [0, π].…

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Q: p = 3 csc()csc (0)

A: find an equation in rectangular coordinates for the EQUATION GIVEN IN SPHERICAL COORDINATES  p=…

Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 2x²y - 4xyz + 6yz²…

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Q: Find both first partial derivatives. xy x² + y² f(x, y): fx(x, y) = (No Response) fy(x, y) (No…

A: Here we have to find the partial derivative.

Q: Find an equation of the tangent to the curve at the point corresponding to the given value of the…

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Q: Rewrite the following equation with the variables separated. 3xy' + 2y = sin(y). dy (sin(y)+2y) O O…

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Q: Evaluate sin'0 cos de Ꮎ

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Q: Consider the following. x = et, y=e-2t (a) Eliminate the parameter to find a Cartesian equation of…

A: Given  x=et  ,  y=e-2t   Then we can find out cartesian curve by eliminating parameter 't' .

Q: 2 √(√sinx + cosx)² dx

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Q: Calculate the first eight terms of the sequence of partial sums correct to four decimal places.…

A: This question can be solved using the concept of convergence and divergence.

Q: 1 n (Inn)3/2 Σ(-1)". n=3

A: Given: Here, an=1n(ln n)3/2≤1n(n)3/2=1n5/2. So, the given series is absolutely convergent by the…