Зх -5 dx (x+1) (x+2)²

Q: Čonsider the following equations. 3 f(x) .3 y = 0 X = -4 х3D —1

A: To find the area of the region bounded by the given curves.

Q: Find the four second partial derivatives. Observe that the second mixed partials are equal.…

A: Given that,      z=19xey-10ye-x

Q: Now, let's discuss the difference cases of solution to a given system of linear equations. There are…

A: Given problem :- Now, let's discuss the difference cases of solution to a given system of linear…

Q: Use Riemann Sums to calculate the area under the curve over the interval (1,3] for f(x) = x² + 2

A: By using Reimann Sums to calculate the area under the curve over the interval 1, 3 for fx=x2+2.

Q: 1 Find the length of the curve y (x2 + 2)3/2 from x = 0 to x =9. 3

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Q: ntinuous function, f (x), has a domain of [-6, 6] -6 <x<-2 x=-2 -2 <x< 0 x=0 0 < x<6 does not exist…

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Q: Preview Activity 1.5.1. One of the longest stretches of straight (and flat) road in North America…

A: Given problem:- Preview Activity 1.5.1. One of the longest stretches of straight (and flat) road in…

Q: Verify Green's Theorem by evaluating both integrals aM y? dx + x² dy = | / (G dA ay əx for the given…

A: Solved below.

Q: 4) Find the critical points of the parametric equations x = t* - 1 y = t3 - t

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Q: mal places as needed.)

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Q: Find V (F x G), if F(x, y, z) = 11xi +j+ 13yk and G(x, y, z) = xi + yj – zk. V. (F x G) =

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Q: Exercise 7.2 1. Calculate the values for f (x) = 3x a) f(2) %3D b) f(-2) %3D is (1; 2; 3). 3. %3D of…

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Q: Find div F and curl F if F(x, y, z) = 10e*Y i – 6 cos yj+ 2 sin? z z k. div F= curl F=

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Q: 3) Find the derivative Of S> Sin (xy) + e' v#5

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Q: Evaluate the triple iterated integral. xyz³ dx dy dz

A: ∫02∫02∫-14xyz3dxdydz=∫02∫02x2yz32x=-1x=4dydz…

Q: Find V x (V x F) if F(x, y, z) = 2xy j+ 6xyz k. %3D V × (V × F) =

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Q: Find V· (V × F), if F(x, y, z) = 5e**i+ 5xe®j – 7ev³k. V· (V × F) =

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Q: ||r(t) x r"(t)|| Use the formula k(t) to find k(t). r(t) = 8 cos(8t)i + 8 sin(8t)j + 5tk к(€)

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Q: e. Suppose someone claims that C'(5000) = -0.1. What would the practical mean- ing of this…

A: We have to find the meaning of C'(2000).

Q: Find the derivative of the following equation: (2x – 1) (3a? + 2) - O 48x + 36x2 + 22x + 8 48x3…

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Q: Find the curvature of r(t) = 5(cos t) i + 12(sin t) j + tk at t = m/2. Ok = 8/13 Ok = 5/13 O k =…

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Q: Solve the given differential equation by undetermined coefficients. y'' + y = 5x sin(x) y(x) =

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Q: The sales function for a product is given by S(x) 124 + 37.8x? – 0.6x, wherex represents thousands…

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Q: n 1) Use the Integral Test to determine whether the series is convergent or divergent. n² +1 n=1…

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Q: Solve the initial value problem y′′−10y′+50y=0 for y(0)=1 and y′(0)=5. After getting the equation…

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Q: Determine whether the improper integral diverges or converges. -6x dx O converges O diverges…

A: This is a problem related to indefinite integral. Based on the general formula and concept we will…

Q: _4. What is the first derivative of f(x) = (x² – 4)(3x – 2)? а. 9х? - 4х — 12 b. (2х)(3) C. 6x d. (x…

A: Topic:- derivatives

Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 <ts 1. x + 3y2) dy

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Q: If a rock is dropped from a height of 193 ft, its poistiont seconds after it is dropped until it…

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Q: (2x – 3y) dx + (2y – 3x) dy

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Q: Find the curvature and the radius of curvature at the stated point. r(t) = 5 cos(t)i+11 sin(t)j+4tk;…

A: Given problem:- Find the curvature and the radius of curvature at the stated point.   r(t) = 5cos…

Q: Use Hooke's Law to determine the work done by the variable force in the spring problem. A force of 7…

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Q: Find div F and curl F if F(x, y, z) = 3y°z°i – 3x*2°j – 3xy*k. - div F= curl F=

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Q: Directions: Compute f'(3) for each of the following function. Then connect item A to item B by using…

A: We have to find the value of f'(3).

Q: Evaluate F. dr. F(x, y) = xi + yi C: r(t) = (3t + 4)i + tj, Ostsi

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Q: Use the following information to answer the question below. lim f(x) = 3 lim f(x) = ∞ lim f(x) = -3…

A: Information of the function is given, we have to find the required values

Q: Find the derivative of the following equation x+3 x-4 (a-4)° 2x (x-4)² 7 (x-4) 2x-1 (x–4)°

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Q: Refer to the graph below. Find lim f(x). 3. 2- 1+ -5 4-3 -2 -1 -1+ 3. 4 5 x -2+ -3+ Does not exist 4…

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Q: Find the four second partial derivatives, Observe that the second mixed partials a z = 19xeY-10ye

A: We will differentiate partially with respect to x and y.

Q: Find V · (F × G), if F(x, y, z) = 2xi+j+14yk and G(x, y, z) = xi+ yj – zk. %3D - V · (F × G) = %3D

A: To solve the following problem

Q: Consider the function f(x) = 9x + 4x-1. For this function there are four important intervals: (- 00,…

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Q: Verify Green's Theorem by evaluating both integrals Lr dx + x* dy = / dA ду x² dy ax for the given…

A: In this question we verify Green's Theorem                 i.e, verify integral  ∫C y2 dx +x2 dy =…

Q: d²y of the following equation then simplify whenever possible. 3) Find and dx dx- x = 3em y = 4e-m

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Q: ||r(t) × r"(t)|| ||r(t)||° Use the formula k(t) to find k(t). r(t) = t'i + tốj K(t) =

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Q: d Calculate ri(t) · r2(t)] and rı(t) × r2(t)] first by differentiating d dt the product directly and…

A: Given

Q: Describe the graph of the equation. r= 2 sin 4ri + 2 cos 4tj O t is a circle of radius 2 in the…

A: Given; r=2sin4t i+ 2cos4t j

Q: 5.) Matching : Match the terms at the right with the best term on the left that matches it. Secant…

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Q: Evaluate: Vt2 + 3 – 2 lim - t→-1 t² – 1 - O Does not exist 1/4

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise.…

A: Given:        ∮C7xydx+4xydy  Where C is the rectangle bounded by x=-1, x=2,y=1 and y=5  The formula…

Q: Sketch the region R and evaluate the iterated integral F(x, y) dA. (1 - 2x + 8y) dy dx 2.0- 2.0 1.5…

A: A detailed solution is given below