16-x2| (a) lim (2 + x) 16-x²| ズ→4+ 4-x

Q: 3. Use the Comparison Test to determine if the series 5n Cos 2n - n³ + n² + 1 n=1 converges or diver...

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Q: eiz-e-iz 1. Show that Sin z 2i

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Q: 1. y= x - x'cosx + 2xsinx + 2cosx

A: solution:-(1)y=x3-x2cosx+2xsinx+2cosxy'=ddxx3-x2ddxcosx+cosxddxx2+2xddxsinx+sinxddxx+2ddxcosx=3x2-x2...

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Q: The relationship between a professional basketball player's height H (in inches) and weight W (in po...

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

A: a) summation of  n/(n3 + 1). b) summation of (n2 + 1)/(n3 + 1). c) summation of n3 / 5n.    

Q: If cos? 0 – 3 cos 0 + 2 = sin² 0 and 0 an acute angle, then the value of (4 cot 0 + 2 csc 0) is V3 8...

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Q: Find the length of the curve over the given interval. r = 7 - 7 sin(0) on the interval 0 < 0 < 2n

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Q: The quantity of a substance can be modeled by the function N(t) that satisfies the differential equa...

A: We have to find the quantity of substance at t=1.8.

Q: True or False: If 3 dx%In|x-3|+B In|x+2|+C (x-3)(x+2) 2 then B =

A: true find integration use partial fraction  

Q: 8. y = In(x + V +1)

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Q: Imagine that at a particular time, a kitchen counter has on it 10 bacteria and that this type of bac...

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Q: (1.5,2) 1.5 (0,7, 0.2Y f0.7,0.2) O.5 to - O.5 -0.57 ー15 0.5 1.5 (-1,2,-1) - 15 -2 does f have the ab...

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Q: A particle moves along the x-axis (units in cm). Its initial position at t=0 sec is x(0) = 15. The f...

A: Acceleration

Q: 2. Use the Integral Test to determine if the series 1 (n+ 2)/4 n=1 converges or diverges.

A: Given problem:-

Q: 2 Determine the equation in the form (x) kx for the function with a vertical %D asymptote at x = 1 a...

A: The function with vertical asymptote at x=1 and y-intercept at -1.

Q: Use the First Derivative Test to find relative (local) maximum points or minimum points, if any, of ...

A: Given problem:- Use the First Derivative Test to find relative (local) maximum points or minimum poi...

Q: g8) = 6x34 54x2+90X Is the graph of g) gx) at X= -12 the graph of ga)is concave up orconcaue down at...

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Q: 2. An object is dropped from a stationary balloon at 500m. (a--9.8m/s²)( a. Express the object's hei...

A: This is a problem related to newton's law of motion. By using general formula of motion's we will ca...

Q: +00 e-*dx

A: Topic = Integration

Q: Let a, b be real numbers and consider the integral (ax² + b) cos(x)dx. Using integration by parts wi...

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Q: 5. Evaluate the folloming integral over the region R 2des places. Gitosetrsine)r dride పా

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Q: Consider the function fix) - sin x. Complete the table below and sketch its graph. 011/6 11/2 Sn/6 7...

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Q: 2 ydx = 3xdy; when x = -2, y = 1 Ans. y = (x/2)3

A: Given: 2ydx=3xdy ; x=-2, y=1   We know that; ∫1ax+bdx=1alnax+b+C

Q: Given revenue and cost functions R(q)=80q−0.2q2 and C(q)=15q+500​, find the quantity that maximizes ...

A: This question can be solved using the concept of maxima and minima.

Q: Question 6 Evaluate the integral J sinh? COSA(2X) +C cost(2x) A sint(2x) B +C sinh“(2x) +C 8 cost4(2...

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Q: Evaluate the integral. Answer should be expressed as a decimal value (5 decimal places, example 0.01...

A: Put y =5secthetha and solve it. 

Q: Determine the following information regarding the function + 2(x - 4)- A. f (x) f "(x) Intervals of ...

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Q: Using integration by parts and taking a > 0, the integral x In(ax)dx is equal to: In a 2 In(2a) - 3 ...

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Q: The 26th term of a Fibonacci sequence is 121393 and the 27th term is 1916418. What is the 24th term?

A: F0=0, F1=1Fn = Fn-1 + Fn-2,  n≥2 F26 =121393F27 =1916418F27 =F27-1 + F27-2F27 =F26 + F25F25 =F27 -F2...

Q: Use the First Derivative Test to find relative (local) maximum points points, if any, of the given f...

A: given 

Q: An equation of the plane passing through A(2,1, –1), B(0,–2,0), and С (1,-1,2) is: 7х — 5у — z %3 10...

A: We have to find an equation of the plane passing through A(2,1,-1), B(0,-2,0), and C(1,-1,2).

Q: dx For (x+x³)(x Tan-!x +1) = In[F(x)]+ C• What is f(/3) if C = 0? 3 V3 6 + 3 +

A: Given:     ∫dxx+x3xTan-1x+1=lnFx+C    =∫1x+x3xTan-1x+1dx substitute u=tan-1x →du=1x2+1dx     =∫cot2u...

Q: The integral dz is equal to 2e + C. Select one O True OFalse

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Q: Use L'Hopitals's rule to find lim (2 – x)tan(ra/2). (Tx x→1

A: We use elogu=u and l- hospital rules in this question to find limit.

Q: y3 Set up an integral that represents the surface area of the surface generated by revolving the gra...

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Q: Evaluate the integral: el/z dx -1

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Q: Obtain the particular solution satisfying the initial conditions indicated.

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Q: Use an appropriate test to determine if the series ) 2n converges or diverges. n+ en

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Q: use second derivaictive to find derivaitve 1 Crihalralues -3 and I (-a3) V(I, I'ntervals ofinerease ...

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Q: The sum of squares of two consecutive odd numbers is 130. Find the sum of the numbers. Let: x = 1st ...

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Q: $ Solve and convert to rectangular form. ti sin sin )

A: Since the student has posted multiple questions and does not mention any specific question, so we ar...

Q: cos x dx 1 - cos? x d)

A: We have to find the antiderivative if the given part d.

Q: I Find the second derivatively") of the following functions and simplity the final results. 1. y=x-x...

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Q: 1 x?g* dx. -1

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Q: Let bn and Cn for all n e N such that n > 2. Determine whether the given n = COS = COS n – 1 series ...

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Q: Whose ares is given by the double Integral. 1 2 5 6 7 1 2 3 4 5 6 7 8 Change the order of Integratio...

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Q: Check if the following is true or false: (x² + 3)dx = 18 %3D

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Q: has

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Q: 10x + 1800 The average cost for a company to produce x units of a product is given by the function A...

A: Given: Average cost for a company to produce x units of a product is given by a function A(x) =( 10x...