(a) lim tan coth an [ coth()] -0+I

Q: Work problem 2 ( } Let w(u, v) = 5u - 5v + u³ - 5v³, u = cos(21) and v = u —sin(3s). Use chain rule…

A: In this question, we will use chain rule to find all the derivatives of w.

Q: Find the directional derivative g(x, y) = x² + y², of the function at P in the direction of v. P(5,…

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Q: Solve the initial value problem: dy dz 9y, y(0) = 1

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Q: Find the solution of the following IVP: y(t) = = dy dt 2ty=9t²e, y(0) = 5.

A: We have to solve the given IVP.

Q: Find the arc length of the following curve on the given interval. x=7t+1, y = 24t-7, 0≤t≤3 The…

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Q: Let f(x) = X x - 3 g(f(x)) = and g(x) = 4 X Find the following functions. Simplify your answers.…

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Q: Question 35 If z = x arctan 0 - 4 OFF O undefined ◄ Previous (²).find əz əx at x = 0, y = 1, z = 1.

A: To find the partial derivative of z with respect to x.

Q: Find the directional derivative of the function at P in the direction of v. f(x, y) = x³y³, P(8, 3),…

A: Here we have to find the direction derivative.

Q: dz Evaluate: ¹5 102 -5 0 1 O Divergent 00 O-1

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Q: lim I→0 √2+11-√11 I

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Q: sider the DE: dy (6x²y² - 10)dx. = the differential equation 1:ss

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Q: Find the point of inflection of the graph of the function. (If an answer does not exist, enter DNE.)…

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Q: Use synthetic division to show that the number given to the right of the equation is a solution of…

A: Given :

Q: Evaluate f cosh² x dx đ (sinh 2 từ t + x) + C O 2r O2e² +42 + C 8 O None of the choices…

A: We have to evaluate  ∫ cosh2(x) dx

Q: Activity 1. Evaluate the following definite integrals by using the fundamental theorem of Integral…

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Q: Given: y Find: y-intercept O P(0, 1) O P(0,1) O P(1,0) 1 (ex + 1)² no y-intercept

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Q: The differential equation dy 6x + 2 da 12y² + 14y + 5 Find such a solution and then give the related…

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Q: S dz zlnz (Inz)²-1 Select one: O A. Q B. O C. Q D. arcsec(Inx) + C arcsin(lnx) + C arccot(Inx) + C…

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Q: PART I. DIFFERENTIALS 1. √101

A: We can find the approximate answer as below.

Q: Farmer Jones and his wife, Dr. Jones, decide to build a fence on their farm. Because Dr. Jones is a…

A: Follow the procedure given below.

Q: Find (²-1) ln(x)dx

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Q: Given: In (sin² 3t) = e = arc cot (w) Find: dw dt O(1+w²) (6cot (36) e) [ Oet+w²et - 6tan (3t) - 6w²…

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Q: Work problem 1 Consider the ellipsoid given by the equation: .8 53 - 5z². X + y 4 8 a) i ]Find the…

A: Let's find equation of tangent plane and normal line.

Q: (c) lim ln(csch ¹x) #+++∞

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Q: (a) √ (e² +2²) dz (b) f 3² dr

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Q: Evaluate the limit: lim, ∞ ○-6 00 ○ 6 e 10-00 최승

A: This question can be solved using the concept of L hopital's rule.

Q: What is the area (in square

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Q: O ди If u = f(x,y), x = g(w) and y = h(w), using Chain Rule, what is aw O ди aw ди Əw || O all of…

A: u=fx,y, x=gw and y=hw

Q: es Ous es les eButton Orations 365 Approximate the value of 22.5 O4+4 In(2) 06 O4+2 In(2) O4 +0.5…

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Q: 1 SSR (x+y)² dxdy

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Q: Consider the indefinite integral fe5z +6 dæ: a) This can be transformed into a basic integral by…

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Q: Use the given information to find the exact value of the expression.  cos θ = 5/13 , θ lies in…

A: Given :cosθ=513

Q: π/2 The integral f/2 So sin drde is equal to cos O-1/2 O 1/2 0 1 00 10

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Q: Find the arc length of the following curve on the given interval. x= 12t³, y=18t², 0sts √3 The arc…

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Q: L 2x²³ + 8x doc 3 √x² + 4

A: This question can be solved using the concept of integration by substitution.

Q: Find an equation of the tangent plane to the surface at the given point. x² + y²5z² = 29, (-3, -5,…

A: Solution of given question is written in below steps.

Q: An open-top box is to be made from a 12-inch by 30-inch piece of plastic by removing a square from…

A: This is  a problem related to maxima and minima. Based on the genera formula and concept we will…

Q: -(4x³y - 16)dy = (6x²y² – 10)dx. A) Show that the differential equation is exact. B) Solve the…

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Q: Part b: We consider the function f(x, y) = x sin y - y cos x + y Find fx(x, y), fxy(x, y), and fxyx…

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Q: 3. fx³ (a²+x²)¹/² dx

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Q: Question 11 Find dy/dx of y = log₂ (x log5 x) In a alna ln 2 O y =

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Q: Use the formula for the general term (the nth term) of a geometric sequence to find the indicated…

A: We have to find the 10th term. The general term geometric progression is given by- an=a1rn-1

Q: Sy²sin (2y) dy

A: Integration by parts.

Q: Choose the direction vector for which the function f defined by f(x, y)= sin(3x) cos(11y) has the…

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Q: Find the derivative of y = arccos x + x 1-x²

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Q: The integral 2 fossin drde is equal to π/2 O-1/2 O 1/2 0 1 00 10

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Q: Given the function f(x, y)= xye+tan² esec2 y The second derivative fyy of f is equal to 0. Select…

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Q: (a) √ (cos r - sin r) da (b) / cot² x da

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Q: Calculate the volume of the solid bounded by the surfaces given by x2 + y2 = 1, z = 0 and z= x2 + y2

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Q: Use the given information to find the exact value of the trigonometric function.  sin θ = 1/4 , tan…

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