Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle. y sin(x), y=x, x= 7/2, X-

Q: sint F(x) = √"* ( *ª*** ( √ ¹ + uª) du) dt Jo

A: The Fundamental Theorem of Calculus says: F(x)=∫ag(x)f(t) dt⇒F'(x)=f(g(x))g'(x)

Q: Q5: Find d for the following functions: dx (1) In(x - y) = xy + y³ ; (2) y = tan³ √cot(7x) ;

A: We can solve the answers as below by finding the derivatives.

Q: 1-). 25 2-) 3+4i 3-1

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Q: Solve the given initial-value problem. y(x) = y" + 6y7y = 11e2x, y(0) = 1, y'(0) = 1 2x -7.x 7e +…

A: We can solve the given initial valued problem .

Q: nd an equation of a plane passing through the following 3 points (1,-1,-1), (-4,1,4), (3,5,3)

A: topic- equation of plane through three points equation of plane passing through three points…

Q: dy Q5: Find for the following functions: dx (3) y = ex.sin² x In√x

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Q: (12) Find the derivative of the function Y = cos (a³ + x³)

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Q: ¡¡y y cos x² dx dy Evaluate the double integral by reversing the order Show your answer in details.

A: Change the order of integration and then  change limits respectively

Q: 0/= log10 (x) dx

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Q: Q5: Find for the following fun dx (1) In(x - y) = xy + y² ;

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 3. Evaluate the definite integral below: S¯¼ √x² + 2x − 5dx + Sq − √x² + 2x − 5dx

A: To solve the following integral problem

Q: Use the tabulated values off to evaluate the left and right Riemann sums for n = 10 over the…

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Q: (g) Determine the minimum or maximum value of the function. (h) Write the domain and range in…

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Q: Q3 :(A): By using "L' Hopital rules "; Find the limits of : (1) limx-ol: 1-cos x sin²x (2) lim, o…

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Q: Write a polynomial f(x) that satisfies the given conditions. 2 Polynomial of lowest degree with…

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Q: 5. j(4x²-5x+4)*(8x-5)dx 6X dx x ²-5

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Q: B. A heavy rock is thrown straight up with a velocity of 160 ft/ sec. The rock reaches a of S=160t -…

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Q: f'(x) = (x+3)(12 - 1)(x - 14) Then the first relative extremum (from the left) for f(z) occurs at z…

A: Since you have posted multipart questions i can do first three subparts as per our company…

Q: Use implicit differentiation for x² + y² O x/y O 5x O-x/y O -5x = 25.

A: To find the derivative.

Q: Find the component form of the vector u initial point (3,8,8) terminal point (5,6,10)

A: Initial point of u is (3,8,8)terminal point of u is (5,6,10)

Q: Find a differential equation whose general solution is 8t y = c₁est + c₂e-2t. = 0

A: We can find the differential equation as below.

Q: Find all the zeros. Write the answer in exact form. q(x)=x²-₁ -7x+14x-6 If there is more than one…

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Q: Find the volume of the solid generated by revolving the region bounded by the curves 3π y = sin x +…

A: Given problem:- Find the volume of the solid generated by revolving the region bounded by the curves…

Q: LI) Prove that (3

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Q: What is 2x2

A: We can answer the question as below.

Q: 3): Find the tangent equation to the curve y = sin² x at point x =

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Q: Consider the following. x = et, y=e-2t (a) Eliminate the parameter to find a Cartesian equation of…

A: Given  x=et  ,  y=e-2t   Then we can find out cartesian curve by eliminating parameter 't' .

Q: Evaluate INIM -6 x³ dx √x²-9

A: To find out the definite integral.

Q: A. B. Evaluate the following integrals using substitution method: (³-1) ²/3 √2 5.² 0 √r sin (1 + x²)…

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Q: 1. / (1 + 3x) dx 5 2. / u² (4 + u°) ³ du

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Q: (a) lim x² - x + 6 X2 x 2 x² + 2x - 3 x² (b) lim x - 6 x 3 x² - 2x - 3 x - 4 (c) lim x+4√√√x-2

A: a.limx→2x2-x+6x2+2x-3=4-2+64+4-3=85b.limx→3x2-x-6x2-2x-3limx→3x-3x+2x-3x+1limx→3x+2x+1=54

Q: Use Gauss-Jordan elimination to solve the given system. 3x + 6y – 3z = −2 -2y + 3z = 1 6x + 6y + 3z…

A: Follow the procedure given below.

Q: Q2: Solve the following integrals: (3) √ √dx dx (4) fxe* dx

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Q: Calculate the double integral. 16 9(1+x²) 1+ y² dA, R = {(x, y) | 0 ≤ x ≤ 5,0 ≤ y ≤ 1}

A: Please see the below picture for detailed solution.

Q: Q2/ A. Find the following limits. Answer four only. i. ii. iii. iv. V. lim x1 x-1 4x-x² lim X-4…

A: To evaluate the limit.

Q: Find dy ду é^sinx in sx

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Q: Q1/ Solve the following differential Equations. 3- dx +2²= 3x x

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Q: Solve the following differential equations: a- (2x + 3y -2) dx + (3x -4 y +1) dy=0 b- (x²+3y²)…

A: The given differential equations are;  1) (2x+3y-2)dx+(3x-4y+1)dy=0 2) (x2+3y2)dx-2xydy=0.

Q: Q2: Solve the following integrals: (1) f 7x²+14x+15 (x²+3)(x+7) 02 dx ; u nein!! sin x+cos x (2) […

A: We have to calculate the given indefinite integral according to the given information

Q: The rate of growth of the population of a city is predicted to be the following, where p is the…

A: topic - differential equation

Q: dp dt Suppose that the current population is 100,000. (a) What is the predicted rate of growth 3…

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Q: Solve the given initial-value problem. y(x) = y" + 6y' - 7y= 11e²x, y(0) = 1, y'(0) = 1 2x 7e -7.x +…

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Q: Find the instantaneous rate of change for the function at the given value. g(t) = 2-1² at t= -6 The…

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Q: Find a power series representation for the function. f(x) = X 8 - x³

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Q: 2: io ue Approximate the area of the region bounded by the graph of f(t) = cos (t/2-5/8) and the…

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Q: Use the figure below to find the exact value of the trigonometric function of angle A. sin (A) 6 A…

A: it is very basic question of trigonometry.

Q: Show your complete solution: Evaluate the triple integral ㅠ pxy 2 L x 0 COS Zdzdydx X

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Q: Consider the graph of the function f(x) given on the next page, which consists of line segments and…

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Q: 3. 4. S 2t (1²+2) ³ 514 √15 +2 - dt =dt

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Q: 4 2 fcsc^x col²x dx S

A: