-x2 + 5 2. y = cos 2x³

Q: Find the indefinite integral and check the result by differentiation. (Use C for the constant of int...

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Q: A storage shed is to be built in the shape of a box with a square base. It is to have a volume of 1,...

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Q: If 0 = 4 then find exact values for the following:

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Q: Of all rectangles with area 25, which one has the minimum perimeter? Of all rectangles with area 25,...

A: We will find the dimensions with the minimum perimeter. 

Q: Graphs of f(x) (solid) and g(x) (dashed) are given below. Use them to find the following ves. Show y...

A: The given graph of functions is as follows:  

Q: (m2 + 1) yy = 1 O = 2V +1+C O = 2tan- (z) +C O = tan (a) +C O y = Va +1+ C

A: Given query is to find the solution of the differential equation.

Q: Find the average rate of change of f(x) = x² – 1 on the interval[-1,0.4]. Give your answer in decima...

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Q: Use the arc length formula to find the length of the curve y = 36 - x2, 0 s x S 6. Check your answer...

A: y=36-x2   , 0≤x≤6let f(x)=36-x2  Then  Arc length =∫061+(f'(x))2dx                                  ...

Q: Write the given expression in terms of x and y only. sin(sin-(x) + cos-1(y))

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Q: 2. Find the derivatives of the following equations: y = sin¬'(1 – t) y = csc-(x/2) y = In(tan¬1 x) y...

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Q: 4. y = 5 cos 4x, 3rd derivative 5. y = 3 tan 3x, 2nd derivative %3D 5. y = 6 csc x, 2nd derivative

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Q: (b) Find the dimensions of a box with a square base with surface area 56 and the maximal volume. (Us...

A: Given  problem:- Find the dimensions of a box with a square base with surface area 56 and the maxima...

Q: 9 checik whether the following statemects are true or False. lif En an is conditionally convergent, ...

A: For (i), Let us take an=(-1)nn. So, the series ∑n=1∞an is conditionally convergent but ∑n=1∞an is di...

Q: 5. Obtain the particular solution for the given differential equation when SHOW YOUR COMPLETE AND CL...

A: topic- differential equations

Q: Use the alternative form of the dot product to find u · v. ||u|| = 35, ||v|| = 45, and the angle bet...

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Q: A Evaluate the following integrals. 1. S2 dx 2. S6x dx 3. f9° dt 4. S-15x dx 5. S(3x - 4) dx 6. S(7u...

A: As per guidelines, I can answer maximum three subparts of a question. Since you have asked for 11 su...

Q: Applications of Differential Equations A certain radioactive material is known to decay at a rate pr...

A: Let's find. 

Q: 2. b. lim a Csinza +cosa sin29) のッb ト Co」?a

A: find limit

Q: en the graph of the function and the x-axis over the given interval, using the prem of Calculus – 2 ...

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Q: The number of bacteria in a culture is increasing according to the law of exponential growth. The in...

A: N(t) =N0 ekt  ...(1)N0 =260N(1)=260 ekN(8)=260 ek8N(8) =2 N(1)260 ek8 =2*260 eke8k =2 eke7k =27k = l...

Q: Use linear approximation to estimate the following quantity. Choose a value of a to produce a small ...

A: The objective of the question is evaluate the value.

Q: -1 sec vo) do

A: We will use substitute method to solve the integral.

Q: Write the partial fraction form of the following expression: 4 x²+15x+56 Note: You are not asked to ...

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Q: Find the general solution of the differential equation y" +2y + 5y = 5 sin(2t). NOTE: Use c, and cg ...

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Q: 1. Find the next item in the pattern. 1, 2, 3, 5, 8, 13, . .

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Q: Derivative OF the FollOwing 1.y sin x)* 2. y-Tex te* 3. d dx ( scextanx t in csccxttanx)

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Q: Find the indefinite integral. (Use C for the constant of integration.) cos. de e2

A: We will find the indefinite integral as following.

Q: Evaluate the integral: S (3x-3 + 3)dx Choose the most appropriate answer. ○ 응z + 3z + C O 2x5 + 3x +...

A: ∫xndx=xn+1n+1+C , C is a constant and for any real number n.

Q: By using substitution, show that x = 4 pi / 6 is a solution to the equation sin (2x) = cos (x). Show...

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Q: a. Write the equation of the line that represents the linear approximation to the following function...

A: Hee, the given function is: f(x)=3ex f'(x)=3ex

Q: Find dy/dx of the function. y=log2 x

A: To find derivative of given function.

Q: Evaluate the integral: 5x/8x² – 1 dx - 5 (8x2 – 1)- + C (8a? – 1)-+ C (822 – 1) + C -(8x2 – 1) + C 8...

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Q: The integral of the given function f- (9- dr Arcsin +C b.+ Arcsin + C c. -- Arcsin +c d. None of the...

A: To find the value of a given integral we use the substitution method 

Q: da = 1+ ey-a+5 || e5 + e#+y C = xe-5 – e-y Option 5 Option 1 C = xe – e-y ea-y None of the Choices O...

A: We know, ∫emxdx=emxm+C, C is a constant and for any real number m.

Q: Find the indefinite integral and check the result by differentiation. (Use C for the constant of int...

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Q: Consider the function 1 1- x4 Write a partial sum for the power series which represents this functio...

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Q: Question 2.5 Limit Progress Check Question 1 Table lim 3 lim x Submit

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Q: Consider the function f(x)f(x) whose second derivative is f′′(x)=9x+10sin(x). If f(0)=3f(0)=3 and f′...

A:   We have to find f(x) and find f(3) using given intial condition

Q: The function f(x) = 2x + 1 is defined over the interval [2, 5]. If the interval is divided into n eq...

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Q: (x²+6y²)dx – 4xydy=0

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Q: A student must select 6 subjects. In how many ways can he do that if there are 13 subjects and 1 is ...

A: This question is from principal of counting.

Q: Assignment: Determine the derivative of the ff. functions. 1. y = 8x5 - 2021, 5th derivative

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Q: In the accompanying figure, arc AB of circle 0 measures 70. If the measure of ZAOB is represented by...

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Q: Find a set of parametric equations for the line passing through the point (6, 0, 7) that is parallel...

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Q: The velocity of a car is f(t)=7t meters/second. Use a graph of f(t) to find the exact distance trave...

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Q: Find the general solution of the differential equation and check the result by differentiation. (Use...

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Q: Letting aa and bb be two positive real numbes such that ab=lab=1, which of the followings is true? I...

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Q: Find the set of solutions for the linear system 3x1 + 4x2 + 5x3 7 || 5x2 + 8x3 -8 Use s1, s2, etc. f...

A: Find your answer below 

Q: 4. The domain of the function f(x) = V3-1 is %3D and its range is. 5. The a-intercept of the line 5x...

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Q: 2, 0 4 Evaluate a. lim f(x) X-4 b. lim f(x)

A: Given:        fx=x, x≤02, 0<x≤14-x2 , 1<x≤4-x+5, x>4