1. Use a parametrization to express the area of the given surface as a double integral and then evaluate the integral: The cap cut from the paraboloid z = 2-x2-y² cut by the cone z = x² + y²

Q: 2x 4. Given the function F (x)= 3 do the following: 4.x +1 a. Find F-1 (x). b. Find dom F and dom…

A: Given,            The function is Fx=2x-34x+1.

Q: Find the value of x such that x satisfies the mean-value theorem at the interval [0. 1] for the…

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Q: 1 Let f(x)= J. dt. Find the derivative f(x). -dt. t4 +5 e2x none of the choices

A: Use the concept of derivative of an antiderivative and simplify.

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

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Q: Consider the series 0 n=1 2+n3 For what values of p does it converge? I. p> 1/2 II. p< 2 O l only O…

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Q: Find the two x-intercepts of the function f and show that f'(x) = 0 at some point between the two…

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Q: Given that x=t3+t and y=3/2t4+t2, find dy/dx, d2y/dx2, d3y/dx3

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Q: Evaluate the following integral using Partial Fractions Method: x3 + x2 dx x2 + x – 2 y :

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Q: Since f'(c) f(1) – (0) f(1) – f(0) = 1, f(c) = 1. We therefore equate f'(x) to 1 and solve for x.…

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Q: –6x-'dx

A: Follow the procedure given below.

Q: Q5) Find volume of body bounded by z² + y² + x² = 9.

A: Explanation of the answer is as follows

Q: Find the value of A which is defined as the angle between i+j and j+ k.

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Q: g"(x) sin(x- 1) X-1 -4 13 h(x) = kr -8x+ 6, -1 10 4e-6-x+5, x>3 8 -1 (E) Find all x value(s) on the…

A: Given

Q: Evaluate the following integral using Trigonometric Substitutions Method: 1- x dx y =

A: Here we have to use the trigonometric subsitution method.

Q: At what rate is the distance between the planes changing? Step 1 Let s denote the distance in miles…

A: Topic:- geometry and application of derivatives

Q: x g"(x) sin(x- 1) X-1 x 3 8. 2 -1 (E) Find all x value(s) on the open interval (-2,5) where f(x) has…

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Q: Find the saddle pointis of the function f(x,y) = x° +y°+i y+4 Oa(5-1) Oc (4.0) & (4,0) Od(0.0)

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Q: All edges of a cube are expanding at a rate of 8 centimeters per second. (a) How fast is the surface…

A: All edges of a cube are expanding at a rate of 8 centimeters per second.a To determine how fast is…

Q: Consider ,- (x3+y²). Evaluate dx² O (9x4+6x)e «³+y?) O (6r²+ 3x)e (x³+y?) O (6x4+9x)e (x³+y?) O…

A: I have stated the used formulas in the solution

Q: At which value of x does the local maximum occur? Ox=3 O local maximum does not exist Ox-1 Ox=5

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Q: Consider the region bounded by the curve v= x2 - 1 and the x - axis over the interval [0,3]. Find…

A: The equation for the x-axis is y=0. Draw the given two curves.

Q: 2. Use a parametrization to express the area of the given surface as a double integral and then…

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Q: (b) Repeat part (a) using 3 subintervals and the velocity at the midpoint of each subinterval. mi

A: answer is in next step

Q: Q5) Find volume of body bounded by z? + y2 + x2 9.

A: Given that - x²+y²+z²=9 =&gt; (x-0)²+(y-0)²+(z-0)²=3² Clearly which is a sphere with radius,r= 3…

Q: 25s^2+202s+25. FACTOR THIS QUADRATIC EQUATION ACCURATELY.

A: 25s2+202s+25=0We know that solution of quadratics equation ax2+bx+c=0 is x=-b±b2-4ac2a Herea=25,…

Q: Q1/ Estimate f (1.72) from the given data using Newton's Backward Difference Formula: 1.7 1.8 1.9…

A: we will use newton backward difference formula .

Q: Let a = 2i – 3j and b= 2j + 3k. Compute for the following: (a + b) · (a – b) None of the choices -8…

A: Here we have to find the dot product.

Q: 1.5 3-y Q1) Evaluate the integral dx dy

A: To evaluate the given integral.

Q: Consider the series 5 + 9 + 13 + How many terms does it take for the sum to be 860? O 21 O 20 O 19 O…

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Q: Q2) Solve the D.E dy – (2x/1- y²)dx = 0

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Q: A particle is moving in space and its position at time t is given by r(t) 4(cos t)i+ 4(sin t)j+ /²k,…

A: Given problem:-

Q: 8. (5x'-4x +8x) dx

A: Topic = Integration As per guidelines , At a time only one question can be answered out of different…

Q: hich of the following choices do the alternative ways for writing an iterated triple integral match?…

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Q: Evaluate: | (cosh²2r+ sinh²2r) dr (A 2r +C 1 -sinh 2r +C 2 B -sinh 4r +C 4 D r +C E None

A: cosh²(2r)+sinh²(2r)= cosh(4r) ∫cosh(x)dx= sinh(x)+C, C is a constant.

Q: Find an arc length parametrization r1(8) of r(t) = (sin(t), cos(t), t). r:(s) = (

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Q: (3-y Q1) Evaluate the integral dx dy using polar coordinate

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Q: Q2) Evaluate the following integral using Trigonometric Substitutions Method: dx y = T9x2 + 16 %3D

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Q: Egay wants to fence a rectangular grazing area along a straight river (no fence is needed along the…

A: Given problem:- Egay wants to fence a rectangular grazing area along a straight river (no fence is…

Q: Evaluate triple integral f, SE Lx? - y?)dz dy dx.

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Q: 3. Find the area of the band cut from the paraboloid x² + y? – z = 0 by the planes z = 2 and z = 6.…

A: Let's find.

Q: 1' 1 3 (e) Show that 5 k=1 k k+2

A: I am attaching image so that you understand each and every step.

Q: QI) Evaluate the integral dy dx using polar coordinate

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Q: Q1) Evaluate the following integral using Partial Fractions Method: y = : x³ +x? dx х2 +x — 2

A: Given: y=∫x3+x2x2+x-2dx   We know that; The Power rule: ∫xndx=xn+1n+1+C And ∫1ax+bdx=1alnax+b+C

Q: Determine the area of the circle whose center is at the origin and tangent to the parabola y = x2 -…

A: y=x2-100from the grapph attached, Parabola cuts X-axis at (10,0) and (-10,0)

Q: Q3) Evaluate triple integral S(x2 -y?)dz dx dy.

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Q: The radius r of a sphere is increasing at a rate of 2 inches per minute. (a) Find the rate of change…

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Q: Calculate the derivative by expanding or simplifying the function. 1 – 2(19t) s(t) = (19t)1/2 (Use…

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Q: 02) Solve the D.E dy - (2x/1-y2)dx 0

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Q: Q2) Convert the polar function r tan20 to cartesian.

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Q: Question 4 -e-*) dx Evaluate: A '+C 2 B cosh x +C sinh x +C D – sinh x +C E None (F -cosh x +C 2

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