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2. g(x) = x sinx - 5 cosx at x=π ans. g'(л) = -π3. f(y) 3sec y tan yans. f'(x)=6sec³y - 3 sec y5. y= sin²(3x²-1)ans. y'= 6xsin(6x²-2)6. P(t)= 4csc(sin3t)ans. P'(t)=-12(cos3t)csc(sin3t)cot (sin3t)

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Calculus

10/23/23

Showing all working, determine whether the following improper integral exists

Showing all working, determine whether the following improper integral exists and if so, find its valueI = ∫ 2/sqrt(x + 5) dx from -5 to 5

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Calculus

10/23/23

calculate the integral question using partial fraction

Find ∫(4x − 1) /(x3 − x2 + 2) dx.

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Calculus Math Physics Precalculus

10/22/23

Where is ChatGPT useful? Where is it not useful?

Where is ChatGPT useful?Where is it not useful?

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Calculus

10/22/23

Find all asymptotes

Given g(x) = x^2 + 2 / 2x - 3, fina all asymptotes of the graph, then draw the graph showing asymptotes as dashed lines.

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Calculus

10/22/23

Find asymptotes of the graph

Given g(x) = x^2 + 2 / x^2 - 9, use limits to find the horizontal and vertical asymptotes. Then drawthe graph showing asympototes as dahsed lines.

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Calculus

10/22/23

Horizontal and perpendicular tanget lines

a. at what point(s) does the graph f(x) - x^3 - 3x have a horizontal tangent line?b. at what point(s) does the graph y=x/x-4 have a tangent line perpendicular to y=1/4 x +1

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Calculus

10/22/23

Find the first and second derivatives

Find the first and second derivates for the following:a. y= 1- 4 square root of x + x^3 / yb. y=3x^2e^xc. y=x^3 sinx

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Calculus

10/22/23

Differentiate the following:a. y=In (5x)b. y= In(5/x)c. y=In (x^3)d. y=(In x)^3e. y=x square root of In xf. y = In x / xg. y=In (sec(In theta)h. y=In sec theta+tan theta)I. y= (x^3 - 3) sure root... more

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Calculus

10/22/23

Differentiate the following

Use the limit definition of the derivatives to differentiate the following: CHeck answer using the power rule.a. f(x)= x^2 + 9x - 2b. g(x) = 8 / square root of x

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Calculus

10/22/23

Find the value of d^2 y

If x^3 + y^3 = 16, find the value of d^2 y / dx^2 at the point (2, 2)

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Calculus

10/22/23

Find dy/dx for the folowing

Find dy/dx for the following:a. xy=cot (xy)b. x^2y=y^9x

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Calculus

10/22/23

Find the slope of the curve

Find the slope of the curve (x^2+y^2)^2 = (x-y)^2 at the point (1, -1)

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Calculus

10/22/23

Use the substitution x=3 cos t, 0 ≤ t ≤ π to simplify the following integral

I'm doing the Mobius assignment hereUse the substitution x=3 cos t, 0 ≤ t ≤ π to simplify the following integral: ∫ 1 / sqrt(9 - x^2)(a) Calculate sqrt(9 - x^2) in terms of t.ans: 3*sin(t)(b) If... more

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Calculus Math

10/20/23

Use partial fractions to evaluate the integral

Use partial fractions to evaluate the integral∫ (4x^3 + 2x^2 + 3x + 2) / (x^2(x^2 + 1)) dx

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Calculus Math Algebra 1 Algebra 2

10/20/23

Suppose that a rocket is launched vertically and it is known that the exaust gases are emitted at a constant velocity of 18.5 m/s relative to the rocket,

Suppose that a rocket is launched vertically and it is known that the exhaust gases are emitted at a constant velocity of 18.5 m/s relative to the rocket, the initial mass is 1.4 kg and we take the... more

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Calculus Math Algebra 1 Algebra 2

10/20/23

Suppose that bacteria growth is modelled by the DE

Suppose that the number of bacteria is observed to double after 4 days, and the estimated carrying capacity is19 times the initial population. What is the estimated population, as a multiple of the... more

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Calculus Precalculus

10/20/23

Find the derivative of the following functions: Write the solution of each number

Find the derivative of the following functions: Write the solution of each number5. y= ½tanh 2x + ⅔coth 3xans. y' = sech² 2x - 2csch23x6. y = sinh2 (3x2 – 1)ans. y' = 6xsinh(6x2 - 2)7. f(z) =... more

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Calculus Precalculus

10/20/23

Use implicit differentiation to find the derivative y' of the following: Wrote the solution of each number

Use implicit differentiation to find the derivative y' of the following: Wrote the solution of each number6.y2e2x + xy3 - 1=0ans. y' =y2 + 2ye2x/ 2e2x + 3xy

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Calculus Precalculus

10/20/23

Find the derivative of the following exponential functions: Write the solution of each number

Find the derivative of the following exponential functions: Write the solution of each number2.y = x²e-xans. y' = xe-x(2 - x)3.f(z) = e²(sin z + cos z)ans. f'(z)= 2ez cos z

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Calculus Precalculus

10/20/23

Use implicit and/or logarithmic differentiation to find the derivative y' of: Write the solution of each number

Use implicit and/or logarithmic differentiation to find the derivative y' of: Write the solution of each number9. x = ln(x+y+1)ans. y' = x + y

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Calculus Precalculus

10/20/23

Find the indicated nth derivative of the following. Write the solution of each number

Find the indicated nth derivative of the following. Write the solution of each number7. 2nd derivative of y = In|cscθ - cotθ|ans. y" = - cscθ cotθ

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Find the indicated nth derivative of the following: write the solution of each number

Find the derivative of the following functions: write the solution of each number

Use implicit differentiation to find the: write the solution of each number

Exercise 3.1. Find the derivative of the following functions: write the solution of each number

Showing all working, determine whether the following improper integral exists

calculate the integral question using partial fraction

Where is ChatGPT useful? Where is it not useful?

Find all asymptotes

Find asymptotes of the graph

Horizontal and perpendicular tanget lines

Find the first and second derivatives

Differentiate the following

Differentiate the following

Find the value of d^2 y

Find dy/dx for the folowing

Find the slope of the curve

Use the substitution x=3 cos t, 0 ≤ t ≤ π to simplify the following integral

Use partial fractions to evaluate the integral

Suppose that a rocket is launched vertically and it is known that the exaust gases are emitted at a constant velocity of 18.5 m/s relative to the rocket,

Suppose that bacteria growth is modelled by the DE

Find the derivative of the following functions: Write the solution of each number

Use implicit differentiation to find the derivative y' of the following: Wrote the solution of each number

Find the derivative of the following exponential functions: Write the solution of each number

Use implicit and/or logarithmic differentiation to find the derivative y' of: Write the solution of each number

Find the indicated nth derivative of the following. Write the solution of each number

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