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Q: Ty csc?y dy is equal to A у coly + | coty dy - Scony dy В у coty — Scory dy —у сoty- —у coty + coty…

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Q: ex-e-x b. Find the inverse function of f (x)

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Q: (b) Using the Power Rule for differentiation, find the derivatives for the following functions: (i)…

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Q: Improper Integral. KINDLY EVALUATE and Identufy whether convergent or divergent

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Q: 2. By differentiation rules , evaluate the derivatives of the following and simplify as possible:…

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Q: Evaluate the line integral -ydx + xdy along the curve C: y? = 30x from (30, 30) to (0,0). NOTE:…

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Q: 3. y = In? (csc2x). Find y"

A: y=ln2(csc2x)

Q: A piece of wire 21 m long is cut into two pieces. One piece is bent into a square and the other is…

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Q: Find the average value of the function f) = 8-7 on the interval [0, 9]. %3D

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Q: Find a value for k that will make the given function a probability density function. f(x) = kz, on -…

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Q: Sketch the region enclosed by y 6x and 4x. Find the area of the region.

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Q: Find the integral. 4 9) x4 In 2x dx A) 391.74 B) -202

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Q: You are given the following information about a termite colony population. The current population is…

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Q: Find y': y = arctan(e2x) 2e2x y 1– e4x? 2e2x y = 1 – e4x %3D 2e2x y 1 + e4x %3D 2e2x y 1 + e4x2

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

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Q: Evaluate the line integral - -ydx + xdy along the curve C : y? = 3x from (3, 3) to (0,0). NOTE:…

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Q: ||r'(t) x r"(t)|| Use the formula k(t) to find k(t). ||r(t)|* 13 r(t) = t’i + t°j K(t) =

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Q: Evaluate F. dr. F(x, y) = xi + yj C: r(t) = (9t + 4)i + tj, 0 sts1

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Q: EXAMPLE 3 Evaluate the following integral. VI- 4.r2 SOLUTION Let u = 1 - 4x². Then du %3D , SO xdx =…

A: We can solve as follows

Q: f(x) z400 g(x) lim where f(r) and g(x) are seen in the graph. 3 S(x) 2 -5 -4 -3 -2 -1, 2 9(x)

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Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = 5 cos(t)i…

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Q: Represent the following equations in R? by a vector-valued functions. Imet gaoglecomis shwing your n…

A: Given

Q: Evaluate the following improper integrals. Tell whether it is convergent or divergent. 1.

A: The given integral,     ∫1+∞dxx

Q: Find the derivative of the function: y = (e**)e Oy = e (e*+ + 1) Oy - (e") (e*+* +1) Oy = (e…

A: We know that derivatives of  d(xn)/dx = nxn-1. And d(ex)/dx = ex.   Here i attached the solution of…

Q: Answer the following questions for the function f(x) = a/a? defined on the interval -4 < x < 5. x+16…

A: We need to find concavity and inflection points.

Q: f(t) 3. Find the function f and a number a such that a + dt = 2 sin x for all x greater than zero.…

A: We can solve as follows

Q: a) Prove If he Given DE Is exact or non-exact Find its General solution

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Q: For the matrix A, find (if possible) a nonsingular matrix P such that P-1AP is diagonal. (If not…

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Q: C sin 2wcos 2wciwv

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Q: Find V. (F x G), if F(x, y, z) = 3xi +j+ 10yk and G(x, y, z) = xi + yj – zk. - V. (F x G) =

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Q: + 3x² 4)dx

A: Given query is to find the value of the integral.

Q: Express py? dA as an iterated integral in the order dydr, where R is the region in the ry-plane…

A: Integral

Q: Consider f(x) = (5x + 11)2022, find: i. f'(x) ii. f"(x) iii. f''(x) iv. fiv (x) v. f°(x)

A: Given, f(x)=5x+112022

Q: ||r(t) × r"(t)|| Use the formula k(t) to find k(t). r(t) = ellti+etj K(t) ||

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Q: 2. (Section 9.2) A refinery produces both gasoline and fuel oil, and sells the gasoline for $4.00…

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Q: Find the derivative, dy/dx: In-2x O y = -() In' 1-4 la > 是 In' x 2/1+2In ४ In' z In z 2w In² z ) In'…

A: This question is based on diffrentiation.

Q: (-x+82.762) 1(x) = 0.5e - 25.7 12 М m(x) — 0.15(х - 90)2 — 25.7

A: To find thee first and second derivative of the functions given.

Q: Find the Maclaurin series for f(r) using the definition of a Maclaurin series. [Assume that has a…

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Q: Differentiate the following function y = e log(4") You may use Insert -> Equation to help you input…

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Q: d f'(3).

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Q: Use the function f and the given real number a to find (f -1)'(a). (Hint: See Example 5. If an…

A: Topic:- trigonometry and application of derivatives

Q: Find div F and curl F if F(x, y, z) = 13y'2*i – 11x°z®j – 7xy°k. %3D div F= 0 curl F=|(-35 z y³ + 99…

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Q: Use Lagrange multipliers to find the extreme values of the function f(x, y, z) = x² +y? + z2 subject…

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Q: Find div F and curl F if F(x,y, z) = x2°i+ 4y°x²j+ 2z²yk. div F=|2° + 12 y? x² + 4 z y curl F= 2 z2…

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Q: Which among the following is false for getting the derivative of an implicit function?

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Q: Find an equation of the tangent plane to R(u, v) = (e" sin u , eº cos u , e¯ ) at the point where u…

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Q: Find the area of the quadrilateral lot shown in the figure below to the nearest square foot. 130 ft…

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Q: æ = (f+ a)soɔ Which among the choices is equal to the dy/dx? In your sc - cos(r+y) A)

A: Given: cos(x+y)=x

Q: dx (х -1)3

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Q: 3. If f(x) = [ v19 +r² dt , find f'(3).

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