a Derivative In Exercises 59-84, find the Finding derivative of the function. 60. y = (x² – 6)3

Q: 2x +1 J (3r – 1) ( + 2x +2) Evaluate: -dx F (z) = 2 In (|3r - 1|) + In (x² + 2x + 2) – 4 arctan (r+…

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Q: dy by implicit differentiation. dx Given In xy+x+y=2. Find

A: lnxy+x+y=2Differentiate w.r.t x1xyxy'+y+1+y'=0xy'xy+yxy+y'=-1y'y+1x+y'=-1

Q: If 54 = the determinant of the matrix below. 3 -4 What is the value of x?

A: We can solve this as follows:

Q: O Evaluate the following integral using Trigonometric Substitutions Method: 1- x dx 2, y =

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Q: Choose the suitable function y1, for the method of reduction of order, to find a second solution y2…

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Q: How/ Find the General solution for dhe following O e %3D

A: The given differential equation is;  e2x(dy+2ydx)-x2dx=0. Repost the next questions.

Q: Find the equation of the tangent line to the curve y =4x-8 at the point (3.-2).

A: Topic = Derivative

Q: 1 In solving the antiderivative of f(x) = by miscellaneous substitution, the substitution z =tan|…

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Q: V9 – 4x2 -dx Evaluate: x2 6/ 4x2 + 2x sin A f (x) +C 4x² + 2 sin () + C -1 V9 f (x) = B 3 None of…

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Q: x2 Fusing trigonometric substitution, Jf(x)dx is transformed into n solving for the antiderivative…

A: Given problem:-

Q: S cot®x csc°x dx Gcot'x -cot"x + cot":) + c B none of the choices Gcot"x - cot "x - cot":) + c…

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Q: Find the values of a and b for the curve x*y+ay =b if the point (1,1) is on its graph and the…

A: Given,            The curve is x2y+ay2=b if the point 1,1 is on its graph and the tangent line…

Q: dy = Solve 2xy r x2 + y? given that y = 0 at a = 1 %3D

A: To find particular solution of D.E.

Q: Consider a function () whose dertvative ') continuous as shawn below Graph of f'(x), NOT f(x) 1 5 -1…

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Q: Find the saddle point/s of the function f(x, y) = x² + y° + x®y+ 4 O a (4,0) & (-4,0) O b.(E -1) &…

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Q: (4x* – r*y +y*)dx + x*dy = 0.

A: Let's find.

Q: dy - = 2/y- 5InlVy+5| +c A) True False

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Q: Describe the graph of the equation. r = 18 cos ti + 4 sin tj -k O Itis an ellipse in the x = -1…

A: Let's find.

Q: 9 – 4x2 -dx Evaluate: x2 (품) (A 9— 4г2 2.x sin- f (x) = +C V9 – 4.x2 - 2 sin- (4) + C 2r В f (x) =…

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Q: (a) Show that the integral test applies, and use the integral test to determine whether the series…

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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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Q: If f(x,y) = x3y + exy^2, find the derivatives of df/dx and d2f/dxdy.

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Q: Find the derivative of f(x) = x In(x) 1- In(x) O In(x) O1+ In(x) O In(x) /x

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

A: Explanation of the answer is as follows

Q: 5xy = 4x²z – 3yz²; yx and yz.

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Q: x2 In solving for the antiderivative of f(x) = Fusing trigonometric substitution, Jf(x)dx is…

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Q: Use a triple integral to find the volume of the given solid. The tetrahedron enclosed by the…

A: Given that the tetrahedron enclosed by the coordinate planes and the plane 7x+y+z=4.

Q: a. Neither I nor II

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Q: :Q: solve the following equations 2X-3Y+Z=-1 X+4Y+5Z=25 3x-4y+Z=2 x=8.7 y= 5.7 z= -1.3

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Q: Find the derivative of f(x) = 33x-1 O 33x-2 In3 O 33x-1 In3 33x In3 32x In3

A: (1). Given: fx=33x-1   As we know that; The Power law; ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x And…

Q: S sin²x cos²x dx 1 sin 4x + C 32 O A none of the choices 1 1 ;sin 4x + C 32 8*+3, sin 4x + C O B

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Q: Which of the following is one of the correct steps to evaluate cos'x dx to obtain the desired…

A: Solving

Q: 1. S cos (3 sin x)cos (4 sin x). cosxdx sec*x dx 2. Jtanx 3. Sr 6 tan*x dx 4. /2 sin5x dx

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Q: Find the maximum point for the function f(x) = 1 + 12x – 4x O (-1, -7) O (2, -7) O (0, 1) (1, 9)

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Q: Jse the vectorized Euler method with h = 0.25 to find an approximation for the solution to the given…

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Q: Question 9 In Sx²/25+ x²dx , we let x= 5sine. (A) True (B) False

A: If x=5sinθdifferentiating On both sides.dx=5cosθ∫x225+x2dx=∫(5sinθ)225+(5sinθ)25cosθ…

Q: csc 2 5x cot 5x dx, can be evaluated conveniently using Trigonometric Transformation. ( A) True…

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Q: Let a = (1,2,3),b = (4, –3, –1),c=(-5, –3,5) and d = (-2, 1,6).Find: %3D а. а+ 5b b. [7c| – |5d| c.…

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Q: dx Evaluate: xV x2 +4 (A None of the given choices ® n Vx2+4- 2 + C x² + 4 +2 Vx²+4-4 +C x² + 4 + 4…

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Q: 2X + Y+ 6z= 9 8X + 3Y + 2Z= 13 X + 5Y + Z= 7 X=2 Y=4 Z=15 O X-1 Y=1 Z=1 O X=1 Y=2 Z=1 O X=4 Y=2 Z=-7…

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Q: -is F (x) xỉ (9x“ – 10) where "a" is equal to The antiderivative of f (x): 30 A 12 6. 1 D None of…

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Q: 1. Find the indicated limit or state that is does not exist lim (3x'y- xy³) а. (x,y)→(1,3) b.…

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Q: 1+2 sec (Vx dx Į Va sin (/æ) tan (Væ) sin (/r sec (Vr and sec (Vx Hint: tan (yx =1. cos (Vx

A: Integration

Q: [a, b, ci] [a2 b2 c2] A, = [d2 e2 2] a3 bz C3 Az = \ds es fal If A, = and are any 2 x 3 matrices,…

A: Here we have to prove the given operations.

Q: Give the VALUE only. No need to include the unit. * A chemical manufacturer sells sulfuric acid in…

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Q: If R is the region enclosed by 36 – 4x? - 4y² = 0 and 2x + 2y?- following sets gives R in the polar…

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Q: -2e dx

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Q: The antiderivative of [Vx²-25 dx is x2 – 25 – sec-lx+ C. A True B) False

A: ∫x2-25xdx

Q: 1 * cot³. CSC2 x3 x2

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Q: Which of the following yields the value 318? 3 (8х + 7у) dxdy 0 °0 (8x + 7y) dydx 0 °0 none of the…

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