Question 4 Evaluate the integral *dx, 2" -+C In2 A +C In2 B 2 -+C In2 D +C In2

Q: (14) = (x – y + 5)? dx dy %3D dy (15) (x² – y²)" – xy = 0 dx dy (16) 2xy = x² + 2y² %3D dx

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Q: 10. f"(t) + 3f'(t) + 2f(t) = 0; ƒ (0) = 1 and f'(0) = 0 %3D %3D

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Q: 8. The acceleration of a particle moving along x-axis at time t is defined by a=4t-12. At t=0, the p...

A: Given: The acceleration of a particle moving along x‐axis at time t is defined by a=4t-12. At t=0, t...

Q: I Find the second derivativety") of the following functions and simplify the final results. 1. y= x ...

A: Differentiate with respect to x. 

Q: Find divergence the vector A (div A) where (A=xz^2+ 3xyz) at a vector (1, * 2, -1)

A: Let's find. 

Q: I. Solve the following: 1. Given: y = 2x - Find: a.) dy/dx b.)y" 2. Given: 16y – 9x? = 144, find y" ...

A: Given  1. y=2x-13+43x-2 if x=22. 3x+4y3=5 If (3,2) To find slope m:

Q: Let a = ci + jand b = 3i + 6j. Find c so that a and b are orthogonal. %3D c = i If L is a line in 2-...

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Q: Find dy/dx of the following functions. A. y = x⁵tan5x B. y = esec2x

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Q: Carbon decays exponentially. How many grams of the carbon will be left in 139 years, if 123 grams we...

A: Initial amount P0=123 grams time t=96 years Amount left after 96 years =P=66 grams Exponential decay...

Q: y- (6+5t-ビア 3.

A: We can find the derivative using chain rule as below

Q: Question 10 What is the integrable form of dx? A du B du du D du

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Q: 0. Reliability of Computer Chips The percentage of a certain brand of computer chips that will fail ...

A: We have an expression: P(t)= 100(1-e-0.1t)

Q: Find the three positive numbers whose product is 27 such that their sum is as small as possible.

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Q: Peter likes to drink coffee once its temperature reaches 60 degrees Celsius and will not burn him. I...

A:   note : i can ans 1st and 2nd part and remaining part not related to this question so pls reroute i...

Q: For S dx -=In(F (x))+C. What is F (/3) if C=0? (*+**) (xtan-(x) +1) A - 6. B 3. D 3.

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Q: cos2x- sin2x cos2x For dr=-F(x)+C What is F(x)? COSX sinx 1. (sinx COSX O (cscx x – secx) ³ CSC) cos...

A: We have to find F(x) by indefinite integral

Q: sinx cosx - e sinx +x The integral -dx may be written as me"sinx + px + ge* +C, where m, n, p, q, r,...

A: The integration of the integral is (cosx-esinx+esinx+x)/esinx.

Q: 3. The diagram shows a cuboid that is formed by bending a long wire of length 336 cm?. h 3x (a) Expr...

A: Given:  The diagram shows a cuboid that is formed by bending a long wire of length 336 cm. To Find:...

Q: Evaluate the integral x Inx dx Select one: Inz -+C Oi In r- a +c 0 in z- +c 3. a Ina O None of them ...

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Q: Perth Mining Company operates two mines for the purpose of extracting gold and silver. The Saddle Mi...

A: Given: The Saddle Mine costs $16,000/day to operate. The Horseshoe Mine costs $16,000/day to operate...

Q: Given revenue and cost functions R(q)=80q−0.3q2 and C(q)=14q+550​, find the quantity when profit is ...

A:

Q: Find the diameter of the of the circle with center at (-5, 3) and tangent to the line 8 – 2x = 2. 2 ...

A: Solution: center (h,k) = (-5,3) tangent to the line x-axis 8-2x=2 so, x= 3 &y=0 (3,0)

Q: Which of the following integrals is equal to the integral / f(3x – 5) dx? 713 f(2) dz 7/3 f(2) dz -2...

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Q: Find the derivative of the function. 3. 2x2 - 5 =イ 4- x %3| y' = ||

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Q: A small town is known to grow its population at a rate proportional to the population at any time. A...

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Q: The slope of the tangent line at any point (x, y) on a curve is 2/x. If the point (9, 3) is on the c...

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Q: What is the integrable form of sin-cos-sin0 de 2 2 du 2 1– u² du cosu du -2 sinu du

A: To write the integrable form.

Q: -5 -4 -3 -2 3 4 3 -4+ 18x For the above rational function f( x) = identify its three inflection poin...

A: It can be solved using differentiation.

Q: sinx sinx +x Cosx - e +e The integral dx may be written as me nsinx + px + qe +C, where m, n, p, q, ...

A: Given that a integration first we solve this integration and then we compare to given equations and ...

Q: 3. Determine whether each of the following series is convergent or divergent using the appropriate t...

A: To check the convergence of the given series.

Q: Solve for the angle in the equation. * a. sin (30 + 72)° = cos 48° b. 4 sin? (§) + 8 cos () – 7 = 0 ...

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Q: 5. y = XArctanx - In Vi+x

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Q: Find two unit vectors in 2-space that make an angle of 45° with 7i + 4j. NOTE: Enter the exact answe...

A: Given :Make an angle of 45° with 7i + 4j

Q: 1. Sketch the graph of the following Quadratic function f(x) = (x- 1)2 -4 and find the following (a)...

A: Given Quadratic Eqaution :  y= (x-1)2-4 Graph : 

Q: cost

A: Please refer to the image below

Q: (c) lim * +1)' sin x X-0 2x lim sinx 5 (d) 20 +sin 0 (e) lim - 8-0 40

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for yo...

Q: 2. Find the vertical asymptote/s of 7.x f(r) : %3D x2 - 3r- 28'

A: Here we have to find the vertical asymptote of the function f(x)=7xx2-3x-28

Q: (1x) +3 . Is-3 Check the continuity of f(x) ={-2x , -3 <x< 3 12 3 (6x + 2 ,

A: Here we have to check the continuity of the given function f(x).

Q: +00 e-*dx

A: Topic = Integration

Q: If 0 be a positive acute angle satisfying cos² 0 + cos“ 0 = 1 then the value of tan² 0 + tan“ 0 is

A:

Q: 2. Evaluate lim -4x+1 X-1 x-1

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Q: Let {an}=1 be a convergent sequence such that a1 = V5 and an+1 V5 an. Compute lim an.

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Q: 4. Starting from the same point, Royden starts walking eastward at 0.5 m/s while Nilo starts running...

A: Draw a schematic diagram of given question.

Q: Find the area of the region bounded by the curve y=1--x? and the x-axis. 8 square units 4 square uni...

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Q: 3. Evaluate the definite integral. Give exact answers S(x² + 2x – 4)dx - a. ~2 2x+1 dx Vx2+x-2 b.

A: Take integration. Follow step 2nd . 

Q: IV. Problem Solving: A. Write the expression as a single Integral = xp(x)f S +xp(x)fT 2. f f(x)dx – ...

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Q: A particle moves along an s-axis with the acceleration function 15 a(t) = Vt + 6t - 4 Moreover, its ...

A: The acceleration function of a particle,at=154t+6t

Q: xtra questions: Find the Derivative of 8 1. y = 10 vx ++ x2 2. y = ta n(si n x) 3. у %3D cot?3x

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Q: +oo 2" Use an appropriate test to determine if the series converges or diverges. n+en n=1

A: We will use Ratio Test for the given series.

Q: Let f(x) = (x - 3)-2. Find all values of c in (1, 4) such that f(4) - f(1) = f'(c)(4 - 1). (Enter yo...

A: topic - mean value theorem