QUESTION ONE 1.1 Use any appropriate method to integrate ∫2x^4(x^2-5)^50 dx [8] 1.2. Differentiate f(x) = loga...

QUESTION ONE

1.1 Use any appropriate method to integrate ∫2x^4(x^2-5)^50 dx [8]

1.2. Differentiate f(x) = loga x from the first principle .[9]

1.3 Find the binomial expansion for sqrt(x^2 - 2x) up to 3 terms for which values of x is the expansion valid? [10]

1.4 Given that z = x + jy, express z=2x - jy in terms of z and or z modulus in a simplest form. [6]

Expert Solution

Please find the attached images for complete solutions of Q1.2 and Q1.3.

Q1.1 is incomplete gives the upper and lower limit of integral.

Colby Messinger answered 2 years ago

Differentiate the following: 1) f(x) = √2x-4. (all under square root) 2) f(x) = x/5-x 3)...

Differentiate the following: 1) f(x) = √2x-4. (all under square root) 2) f(x) = x/5-x 3) y=cos(4x^3) 4) f(x)=tan(x^2) 5) f(x)= 3e^2x cos(2x) 6) y= sin2x/cosx 7) y= √sin(cosx) (all under the square root)

1. Use the derivative function, f'(x)f′(x), to determine where the function f(x)=−2x^2+14x−8 is increasing. 2.Use the...

1. Use the derivative function, f'(x)f′(x), to determine where the function f(x)=−2x^2+14x−8 is increasing. 2.Use the derivative function f'(x)f′(x) to determine where the function f(x)=2x^3−27x^2+108x+13 is increasing. 3.Use the derivative function f'(x)f′(x) to determine where the function f(x)=2x^3−27x^2+108x−12 is decreasing. 4.Find each value of the function f(x)=−x^3+12x+9 where the line tangent to the graph is horizontal. x=

I Integrate x^2 e^(-.5(x+1))^2 dx from -infinity to +infinity

Use the secant Method to find a root for the function: f(x) = x^3 + 2x^2...

Use the secant Method to find a root for the function: f(x) = x^3 + 2x^2 + 10x -20, with x_0 = 2, and x_1 = 1.

Problem 2. Use the FFT algorithm to evaluate f(x) = 8 − 4x + 2x 2...

Problem 2. Use the FFT algorithm to evaluate f(x) = 8 − 4x + 2x 2 + 3x 3 − 5x 4 − 4x 5 + 2x 6 + x 7 at the eight 8th roots of unity mod 17. You may stop using recursion when evaluating a linear function (a + bx), which is easier to do directly. The eight 8th roots of unity mod 17 are 1, 2, 4, 8, 16, 15, 13, 9; it is easier to...

Evaluate the integral (x^3+2x^2-4x+5)/(3x^2+x-10)dx

consider f(x) = ln(x) use polynomial degree of 5!!! a) Approximate f(0.9) and f(1.1) b) Use...

consider f(x) = ln(x) use polynomial degree of 5!!! a) Approximate f(0.9) and f(1.1) b) Use Taylor remainder to find an error formula for Taylor polynomial. Give error bounds for each of the two approximations in (a). Which of the two approximations in part (a) is closer to correct value? c) Compare an actual error in each case with error bound in part (b).

let f(x)=(x^2 + 2x) / (x - 1)^2 a) Find the domain and if any intercepts...

let f(x)=(x^2 + 2x) / (x - 1)^2 a) Find the domain and if any intercepts b)find the horizontal asymptotes c) find the vertical asymptotes d)find the intervals on which the function is increasing and decreasing and identify the function's local extreme values, critical values e)identify the concavity and if any the point of inflection f) graph the function

If f(x)=2x^2−5x+3, find f'(−4). Use this to find the equation of the tangent line to the...

If f(x)=2x^2−5x+3, find f'(−4). Use this to find the equation of the tangent line to the parabola y=2x^2−5x+3 at the point (−4,55). The equation of this tangent line can be written in the form y=mx+b where m is: ???? and where b is: ????

Use the method of Lagrange multipliers to find the extreme values of f(x, y) = 2x^2−3y^2...

Use the method of Lagrange multipliers to find the extreme values of f(x, y) = 2x^2−3y^2 subject to the constraint that x^2+y^2 = 3.

Question