(2, 4) y = 2x ng a vertical element of area, he area of the shased region is gven by the integral

Q: Find the area of the shaded region. x = -y x = 2 – y? -2 A B 10 2. 2. 3.

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Q: Find the first derivative with respect to the domain variable for the following functions. 4. f(x) =…

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Q: Problem 11. Solve the following system and express your solutions (if any) as individual ordered…

A: 3x2-2y2=-5     2x2+4y2=18

Q: Show that the function f defined by (x, y) = (1, – 1) f(x, y) = 1² + y (x, y) # (1, –1) I + Y is not…

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Q: S cos³ 3x dx

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Q: Q3 : prove that : cosh?x + sinh²x =coch2x

A: L.H.S.:=cos h2x +sin h2x=(cos hx)2 +(sin hx)2  =ex+e-x22+ex-e-x22=14(ex+e-x)2+(ex-e-x)2

Q: Find the constant a, such that the function is continuous on the entire real line. ( 2x², f(x) = if…

A: Given the function is f(x) = 2x2,if  x≥1ax-1,if  x<1

Q: 4. Show that y=e²* sin 3x satisfies the equation: y" – 4y' + 13y = 0 %3D

A: Topic = Differential equation

Q: Solve the system of differential equations.

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Q: (D² +1)y = sec x. %3D

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Q: 1. The approximate value of -31.8 using linear approximation O -2.0025 O None of the choices O…

A: Ni

Q: 1 æ(ln æ)² de

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Q: In +4 7n+4 Let 2 5" and an 5" n=1 an+1 a) Find lim an n + 00 7n+4 is n =1 5" b) Determine whether 2…

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Q: Find V · (V × F), if F(x, y, z) = 3e"*i+3.xe"j – 8ev²k. V ·(V × F)

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Q: Evaluate the definite integral. i-ej+ k 7 O el - 1 7. O el - 1 i+ (e- - 1) j+ k i- (e-- 1) j+ k O e…

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Q: Colleen's office equipment is depreciating at a rate of 9% per year. She paid $24,500 for it in…

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Q: 3/2 x*(G²- x²) %z

A: …

Q: -12 1. ("(25x – 46x + 3)dx -12

A: topic- definite integral if f(x) is a odd function∫-aaf(x)=0

Q: Evaluate the limit 9х + 5 lim z+00 2r2 – 6x + 6

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Q: Given f"(x) = 7x – 3 and f'(-2) = -6 and f(-2) = 6. Find f(4) %3D |

A: Here we will find f(4),

Q: Find curl (7z i + 8xj+2y k). curi (7z i+ &x j+ 2y k) = (1 i+( j +( )k

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Q: Problem 3. at a speed of 60 cm/s. Suppose the function g models the radius as a function of time t…

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Q: Find V· (V × F), if F(x, y, z) = e®²i+ 4xe®j – 5eV²k. V.(V × F) =

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Q: Q2/A) Find the particular solution for the following D.E., the boundary condition is (y-0@x

A: The given equation is dy=ex-ydx.

Q: Solve the equation on the interval 0s0<2x. 50 = 2 sec 50 What are the solutions to sec T=2 in the…

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Q: Find the limit. If the limit does not exist, type DNE. lim (1,9) →(-4, -2) 32 – 5zy =

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Q: Describe the graph of the equation. r = 7 cos t i - 16 sin i j+k O An ellipse in the planex = 1,…

A: We have to describe the graph of the equation.

Q: 2c dc Te4lnc + 4

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Q: Answer the following True or False: Let f(x) be a differentiable function, such that f(– 1) = - 5…

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Q: State where the power series is centered. (-1)"(2n – 1) „n Σ * 2"n! n = 1

A: Solving

Q: 33) Find the ared ef the Suriface formed by revolving f10) =10 Coso tue cirele r= about tue line Q=…

A: We have to find the surface area.

Q: o) rind all veluees of x for which fue Canveryes. for there helues of x, wnite tul fum of tue senes…

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Q: Q1: find dx of the following statement: a) y = cos? sec

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Q: Find r'(t). r(t) = (tan-'(11t))i+t cos(t)j – Vfk NOTE: Enter your answer in terms of i, j, and k.…

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Q: 15. Evaluate the following double integral. Si (xy* + x)dydx

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Q: alculate the Laplace transform of each of the followir a. 7t b. e' sin(t) c. u(t - 3)e2

A: We can  solve 2 problems only.

Q: Find a power series representation for the function. (Give your power series representation centered…

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Q: petdo eidj to noitom paidi b noit t no eog edt bnt Use the limit process to find the area of the…

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Q: Find the derivative with respect to x. (c) y = v7x – x4 (d) y = (1+ sin 7.x)-5 (a) y = (5x – 2)*…

A: This question is related to derivative, we will solve it using given information.

Q: Question 8 of 10 View Policies Current Attempt in Progress Find r'(t). r(t) = (tan(9t))i+t cos(t)j…

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Q: 2)

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

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Q: Determine the convergence or divergence of the series using any appropriate test from this chapter.…

A: This question can be solved using the concept of geometric series test and p series test for…

Q: Problem 3. A stone is dropped in a lake, creating a circular ripple that travels outward at a speed…

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Q: Use the figure to evaluate the following function, given that f(x) = sin x. (Simplify your answer.…

A: Given diagram,

Q: d Calculate r:(t) - r2(t)] and r:(t) x r2(t)] first by differentiating [ri(t) × r2(t)] first by…

A: Given that     r1(t) = cos(t)i + sin(t)j + 8tk    r2(t) = 7i + tk

Q: Show that g : B → A, g(x) = √ln x is the inverse of f. Why is f^−1(x) 6 ≠ −√ln x?

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Q: d d Calculate r1(t) · r2(t)] and dt ri(t) × r2(t)] first by differentiating dt the product directly…

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Q: ||r'(t) × r"(t)|| Use the formula k(t) to find k(t). ||r(t)||³ r(t) = t’i+ t°j K(t) :

A: We have to find the value of k(t)

Q: Determine the convergence or divergence of the series. (If you need to use co or -0o, enter INFINITY…

A: limn→∞ sech(n)=limn→∞ 2en+e-n=limn→∞ 2e∞+e-∞=limn→∞ 2∞+0=0limn→∞ sech(n)=0