1. Find the smallest distance from the point (0, c, 0) to the surface y = x² + z².

Q: n²2" n=1 a) Show that the series is convergent

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Q: dz and dy dz Suppose z is a function of x and y, and tan Vy² + x2 = 2"e®y_ Solve for

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Q: Use the limit comparison test to determine if the series converges or diverges. 00 22) E 6n3/2 + 7n…

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Q: e4z+1 dx e2r – 1 17.

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Q: Let F(x) = f(f(æ)) and G(x) = (F(x))² . You also know that f(3) = 6, f(6) = 2, f'(6) = 5, f'(3) = 15…

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Q: After substitution is performed, which of the following is equivalent to (4r249)7 dx? 45 8 du u? 13…

A: We have to use the u subsitution method

Q: Find the conservative vector field for the potential function by finding its gradient. f(x, y, z) =…

A: Given : f(x,y,z)=9x2y+5z2   To Find : Conservative Vector field by finding it's gradient

Q: 4. A live oak tree casts a shadow 58 feet long, Find the height of the tree if the angle of…

A: Here is the solution:

Q: Ql: If f(s,t) = s²t+ In(t² – s) find the value of a) atas Q2: For the following function prove that…

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Q: Identify whether the given is a discrete or continuous variable. 1.The temperature of a cup of…

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Q: 7 Determine the intgral

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Q: Given: R. 23 30° A R= 04 v3 02 v3 B.

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Q: Find the length of the curve z(t) = e“ cos(t), y(t) = e“ sin(t) for 0<t<7. %3D Give an exact answer,…

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Q: Determine convergence or divergence of the alternating series. 24) E (-1)n 6n5 + 5 n = 1

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Q: 3. Which of the following integrals requires integration by parts? A. S csc°0 de B. S cot*0 csc*0 do…

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Q: 1. (sin x(cot x) = cos x OSX L.S. R.S.

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Q: Let F(x) = f(f(x)) and G(x) = (F(x))². You also know that f(9) = 7, f(7) = 3, f'(7) = 9, f'(9) = 5…

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Q: -1 Su(u² + 3)! du

A: We need to solve integral.

Q: Find the limit, If it exists. x- 1 lim X---

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Q: Use the properties of the derivative to find the following. r(t) = ti + 5tj + t?k, u(t) = 5ti + t?j…

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Q: 9. Verify the identity 1 1 = 2 sec² x 1-sinx 1+sin x

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Q: 2 2 2 2 4' 16' 64' 256' 1024

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Q: Find the volume of the solid generated by revolving the area bounded by the given curves about the…

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the…

Q: P1:

A: Solving

Q: Identify the function and interval which does not meet the conditions for applying the Mean Value…

A: We have to solve above question

Q: 12. y" +y = séc' x tan x.

A: Let's find.

Q: 元 店sit sin? 4x cos² 2x dx

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Q: Simplify the complex number. Express your answer in a+ bi form and include each step necessary in…

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Q: Let f(x) = Vx? + 9. Then f'(x) is f'(1) is f"(x) is and f'"(1) is

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Q: Use the graph of the parabola to fill in the table. (a) Does the parabola open upward or downwa O…

A: a.   Parabola opens downward   b. Coordinate of vertax. Is (-2,-3)

Q: is a function of K, and y, and tan - z*e®Y.

A: Given problem:- Z is a function of x and y tan√(y2+x2) =zx e6y  To find:-

Q: Step Solve for c. Use inverse trigonometric functions to find the value of c guaranteed by the Mean…

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Q: Let F(x) = f(x*) and G(x) = (f(x)). You also know that a' = 5, f(@) = 3, f'(a) = 13, f () = 1 Then…

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Q: y y =x - 4 y =/2x + 8 4 6 10 x -2- -6+

A: Area bounded by the curves :   If f(x) and g(x) are two continuous function on a,b and f(x)≥g(x) on…

Q: Find the derivative of: 3 sin (– 3x). Hint: sin (x) = [sin(x)]"...so use the chain rule (twice!).

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Q: f(x)= sin (x² +2x)

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Q: y = 4 (2,4) A y = 2x x = 2 B y =x (0,0) Region A is bounded by the lines y= 2x, y= 4 and the y-axis.…

A: Note: As per our company guidelines we are supposed to answer the first three sub-parts of the…

Q: Find div F and curl F if F(x, y, z) = xªi – 2j + yzk. div F= curl F=

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Q: An auto weighing 1,500 pounds is on a street inclined at 10" with the horizontal. Find the force…

A: Let's find.

Q: 6. Compute and write the slope of the tangent lines to dx y - xy +6 = 0 at the point (5,2). a. b. 2y…

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Q: For which value of x is the function f(x) = X - 4 undefined? 2х - 8 O.4 04 1/2

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Q: Differentiate f (x) = 71n(x²-6x+3) A. (2x – 6) 7ln(x²-6x+3) f' (x) = x2 – 6x + 3 - В. In(7) (2x – 6)…

A: Given query is to find the derivative of the expression.

Q: Evaluate the definite integral. I' i+e¯*j+tk )dt O !! k 11 (ell – 1) i – (e- – 1) j + - k O ell – 1…

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Q: L x² cos 2x³ dx? After substitution is performed, which of the following is equivalent to

A: Given that the integrals  To find the evaluate and choose the correct answer

Q: If f(x) = 4/@ln(æ), find f'(x). %3D Find f'(2). Submit Question

A: Given query is to find the value of the derivative at indicated point.

Q: C6. If FCX) =3x-4,43 li find F'(xland f"(x)

A: We need to find the first &amp; 2nd derivative of the given function

Q: (c) F to

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Q: Solve the following differential equations: d³y dy d?y 3- + 3 dx2 В. dx3 dxy=4e*

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Q: An open box is made from an 8 inch x 8 inch piece of cardboard by cutting equal squares from each…

A: Volume of the box

Q: S cosh(5x – 7) dx

A: The given integral is:∫cosh5x-7dx