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

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Q: 1. f(x) = 8 sin x

A: Since you have asked multiple question, we will solve the first question for you as per our guide li...

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Q: Use mathematical induction to show that: 1 2 + 2 2 + 3 2 + ⋯ + ? 2 = (?(?+1)(2?+1)) 6

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Q: 1 determine whether it converges or whether it diverges. As part of your 6. For the series k3' k=0 s...

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A: Given,           The radius of a circle is increasing at the rate of 4 cm/s. And the radius is 5 cm ...

Q: 3. Determine the exact value of f"(0) for f(x) = (cos5x + 5x²)*.

A: Given 

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A: We have to find the Laplacian at the guven point.

Q: Use the method of substitution to find the indefinita integral. Check your resuk by afferentiating. ...

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Q: 7. y = 4 e2x, 4th derivative 8. y = -5 e3x^2, 2nd derivative 9. y = 7 In 7x, 2nd derivative

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Q: Given f(x, y) = 6x²y – 5xy*. Compute:

A: This question is based on Partial differentiation.

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given ...

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given ...

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Q: Consider the points A(3, –3, 3), B(4, –5, 0), C(-3, –4, 0), and D(6, 2, –6). Find the volume of the ...

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Q: Consider the following function. f(x) = x5 – 2 (a) Find the inverse function of f. f-1(x) = %3D

A: The given function is f(x)=x5-2 we have to find the inverse of the function of f. f-1(x)=?

Q: Test the series for convergence or divergence. 1 4. In 3 1 + In 4 1 1 + In 6 In 5 In 7

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Q: Given that log(5) ≈ 0.6990 and log(4) ≈ 0.6021, find the value of the logarithm. log(5/4)

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Q: sin x 5. Use series to evaluate dx .

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Q: 1+ 2+...+n 2. Let n be a positive integer. Evaluate lim if possible. If not possible, explain n2 why...

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Q: y" + 2y' + y = 7 + 75 sin 2x

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Q: Find sets of parametric equations and symmetric equations of the line that passes through the given ...

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Q: f"(x) = 13r- (x²-1)a 2.f(x) = f'(x) = r* +1) 4x (x²-1)2 Determine the intercepts. Determine the equa...

A: f(x) =2x2x2-1Intercepts:x=0, y=0(0, 0),y=0, x=0X and Y-intercept: (0, 0)Asymptotes:x2-1=0x=1, x=-1  ...

Q: Evaluate lim, 0 (1 - )2". (Hint: take log) 6.5 O 1 O 2 O e?

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Q: 5) Find the distance from D to the plane containing A, B, and C NOTE: Enter the exact answer. Distan...

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Q: e5x cos e5x dx sin²e5x

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Q: To pay for a 19,300 motorcycle, Keith made a down payment of 4500 and took out a loan for the rest. ...

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Q: Q1.Find the general solution of following PDE equation (a) (5z+ R)uz + (7x+ R)u, R (b) (z + R)u, + (...

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Q: Find the radius of convergence, R, of the series. ř n(x – 4)" n=1 n° + 1 R = Find the interval, I, o...

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Q: – sin x show that - In |sec x +c ??? %3D COS X

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Q: The rate of growth dP/dt of a population of bacteria is proportional to the square root of t, where ...

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Q: 2 y = 12 – 3x", y = 4 – x 2

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Q: e² sin® (e²) cos' (e²)dx

A: According to question,Given Integral,Let I = ∫ ex sin6ex cos7ex dx

Q: A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular windo...

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Q: *B: %3D A 3. B[ 2 3

A: Find your answer below 

Q: Consider the following graph. y 5 -3 -2 -1 3 -5 -10 Identify the parent function represented by the ...

A: Given problem:-

Q: Find the maximum and minimum values of the function f(x, y) = 2x² + 3y? – 4x – 5 on the domain x² + ...

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Q: expenditures were $1588.08 billion in 2002. a. Find a function that gives the total expenditures x y...

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Q: (x2 – x + 1)y = 4(1 – 2x)y O y = (z? - a + 1)* + C O y = C(x? - a + 1)-4 O y = C(x² – x + 1)4 O Iny ...

A: We know, ∫ dx/x = ln|x| + C , C is a constant. ln(a)+ ln(b)= ln(ab) b*ln(a)= ln(a)b  

Q: Let F(x) = f(x) + g(x)e* + h(x)e²×+ C be the antiderivative of G(x) = (x+ e*), Determine the value o...

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Q: Find two unit vectors in 2-space that make an angle of 45° with 10i + 3j. NOTE: Enter the exact answ...

A: The given question can be solved as shown in step2

Q: Q1 Consider the plane curve defined by the parametric equations x = p + t sin(t),y= p² + t cos(t). C...

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Q: Find a polynomial of degree n that has only the given zero(s). (There are many correct answers.) x =...

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Q: 2. The position function of a particle is given by s(t) = (t – 1)²(t – 3) , where t is measured is s...

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

A: The integral is ∫4+1t31t2dt

Q: x2ex b. Evaluate lim by using T.E. X-0 CoSX-1

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Q: Determine whether the integral is convergent or divergent. If it is convergent, evaluate it. (If the...

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Q: Find the limit as a number, o, or -o. Otherwise enter DNE. lim VnV5n+1 - V 5n |- [(u5

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Q: Consider the following. f(3) = 9, f(-1) = -11 (a) Write the linear function f such that it has the i...

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