The cylindrical coordinates of the point with rectangular coordinates (-V2, -v2, v2) are (v2, , V2). 4 Select one: OTrue O False

Q: Find r'(t). r(t) = (tan-(4t))i+t cos(t)j – Vtk NOTE: Enter your answer in terms of i, j, and k.…

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Q: 1 Σ 'n² +1 ln + 30 1 4 + 9 27 81 243 729 8 16 9

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Q: Integration of (sin(x) + cos(x)) e^x is ______________.

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Q: Find the area of the specified region. 5) Inside the limacon r= 8 + 2 sin 0

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Q: Consider the function f(x) = cos(3 x). (a) Give the derivative of this function. f'(x) = | (b) Find…

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Q: =

A: We will find the derivative.

Q: Select all that apply. Select the functions whose value is zero. sec 270° Csc 360° tan 90° cos 270°…

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Q: Find the derivative of function f given by S(1) = =! X-1 3 x+3'

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Q: 3. Find the binomial series for (1+x)3 4. Use the result in problem 3 to give a power series…

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Q: If f(x) = sin (a*), find f (x) Find f'(5)

A: Given function is f(x) = sinx3 we have to find the first derivative of f(x) that is f'(x).

Q: Find the equation of the tangent line to the graph of y = x3 + 3x2 + 2 at its point of inflection

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Q: Find the curvature and the radius of curvature at the stated point. r(t) = 11 cos(t)i+ 9 sin(t)j +…

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Q: Waat is the degree of the following differential equation? dx dy + x²y dt? d"z = xyz dt? 3 2 O 1

A: The given problem is solved below in detail.

Q: Co. If FCx)=3x-4,+4+1,finelf(xland f"(x)

A: To find out f'(x) and f"(x).

Q: the derivative of f(x) = x% (x% +x% + x%

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Q: Which of the following differential equation has the same order and degree? [dy]6 + 5y = e* A. + 8…

A: See the answer below

Q: 1. Which of the following integration techniques should be used to evaluate f. sec? x V4 - tan? x}…

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Q: Solve the equation xydx - (x + 2)dy = 0

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Q: dx The integral of the given function ſ is equal to (x²–2x+4)ž а. 1/4 b. 1/5 с. 1/6 d. 1/3 e. None…

A: A detailed solution is given below

Q: Select the correct answer. For which pair of matrices is s A B#BA, OA. A=[}2] B = A = 2 B= A = 2 B=…

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Q: Use the Shell Method to find the volume of the solid obtained by rotating region under the graph of…

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Q: Find dy for the given values of x and Ax. y = 5x° - 9x, x= - 2 and Ax= 0.2 dy =D %3D (Round to the…

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Q: x" Find radius and Σ Va3" 9. convergence and interval for this series n=1 n

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Q: a. 0 =-45 → graph type = b. r= 8-8cos0 graph type = facing up/down/left/right? loop length = c. r=…

A: (a) θ=-45°Graph type straight linesymmetry along first and third quadrant     (b) r=8-8cosθgraph…

Q: Solve the equation (2xy - tan y)dx + (x^2 - x (sec y)^2))dy = 0

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Q: 3. For curve y ==x +4x2 - 12x , locate the possible maximum and minimum %3D points.

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Q: Use Lagrange multipliers to find the point on the plane x – 2y+ 3z = 6 that is closest to the point…

A: Let, the point be (x,y,z) then the distance between (x,y,z) & (0,1,4) is:…

Q: Differentiate x + y = e2x+2y A. 1 – 2e2x+2y 1+ 2e2x+2y y' В. -1 + 2e²x+2y 1 – 2e2x+2y y' | С. ||

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

Q: 2. A 15-meter-long ladder is leaning against a wall The bottom of the ladder is pushed horizontally…

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Q: Suppose the table below gives the velocity of a moving object at any time t. Note that 7 IS measured…

A: We have to find the distance and graph of v(t).

Q: 4x 9. sech(2x) dx e

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Q: V. Determine all the relative minimum and maximum values, and saddle points of the function h…

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Q: Find the curvature of the curve 7 (t) = (2 cos(t), 2 sin(t), t) at the point t = 0 Give your answer…

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Q: 12. A force of 170 N is applied to move an object 90 m horizontally. If the force is directed 33°…

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Q: 3) Find an equation for the tangent line to the graph at the specified value of x. y=x²V5-x² ,x=1

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Q: V. Determine all the relative minimum and maximum values, and saddle points of the function h…

A: Solution: Given data, h(x,y)=x3-3x+3xy2

Q: Find the curvature and the radius of curvature at the stated point. r(t) = 9 cos(t)i + 7 sin(t)j +…

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Q: (4, 4) y= 2x-4 (1,-2) Jsing a horizontal element of area, the area of the shaded region is given by…

A: As required, draw a horizontal stripe as shown:

Q: Step 2 Fx) dx = 1 To evaluate f(x) dx, substitute f(x) c In = - Therefore, f(x) dx =

A: We have to evaluate given integral

Q: Complete the equation. V-14x ). arccos X- 7 = arctan 7 <x < 14 7

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Q: y =x und y = x+2 ... evolve the area about the line x 3. Using cylindrical shell method, the volume…

A: The cylindrical shell method gives the ,Volume on revolution about a line is given by…

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

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Q: csch 3x – 5 [3х — 10. dx V3x – 5

A: 10) To evaluate: I=∫csch43x-53x-5dx Substitute 3x-5=u⇒123x-5(3) dx=du⇒13x-5dx=2du3 ⇒I=∫csch4u2du3…

Q: d Calculate ri(t) · r2(t)] and d ri(t) x r2(t)] first by differentiating dt' dt the product directly…

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Q: 3n° + 2n³ - 7 {a,}== 7n' + 3п +4

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Q: dr 1/4( In 4) o 1/( In 4) o In 4 In (4) 1/4

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Q: 17. The base of a triangle is increasing at a rate of 2in/min. If the altitude is always twice the…

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Q: 26 State the Fundamental Theorem of Calculus . you must state the first and the second fundamental…

A: On solving this we will get

Q: 1. For the curve x2y2 = 25 at (-1,-5), find the equation of the normal line.

A: The given curve is: x2y2=25 Differentiating it with respect to x: y22x+x22ydydx=0 at (-1,-5):…

Q: f4) = (/4x² +8 - x²)* (8x + 4x)V4x2 + 8 - 24x - 32x V4x2 +8 If then f'(x) =

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