Q3 The vertical distance travelled by a rocket from x = 8 to x = 30 seconds is given by: s = ° (2000 In 140000 |140000–2100t |- 9.8x ) dx (a) Compute the vertical distance covered by the rocket by using the Simpson's 3/8 rule with n = 3. Given t = x. Correct up to 4 decimal places. (b) Compute the relative true eror for the integral above. Given, True value = 11061.34

Q: 1. Find the instantaneous rate of change when x=π for y=sin*x/2-3cosx.   2. Interpret geometrically…

A: Simply take the derivative and put the given point to find the instantaneous rate of change.

Q: 2 3/2 between x = 0 and x = 1 is 3 %3D The length of the curve y =

A: We will find out the length of curve.

Q: If f(z) = (iz? + 3z?)³, find f'(z), when z = 2i. %3D

A:

Q: The instantaneous rate of change of a ball (in ft/s) is given by f'(x) = √x Select one: 1 4 O a. sec…

A:

Q: 3 Estimate dx using right endpoints for n = 3 approximating rectangles. 3 dx is approximately

A: Integration

Q: J(2,5) has been dilated to J'(3,7.5). What scale factor was used in this dilation?

A: scale factor =x'x or =y'y

Q: sqrt(4-4x2) from 0.5 to 0.6 using inverse hyperbolic functions

A:

Q: i) S, (x Inx)³ dx. ii) S •1 3 In) dx.

A:

Q: Find an approximate value of 8. [6x 6 x dx

A:

Q: Find of xy = cot(xy) dx

A:

Q: e"(cosh(2t)-cosh(5t))dt = ? -St

A: We will evaluate this integral using Laplace transform definition.

Q: Find dy/dx for the Following!- secx 13x Cot 5x (2In 9x)

A: Find dydx of the following:y=lnx4secxtan-1e3x6cot5xe2ln9x

Q: Differentiate implicitly to find: dy/dx ln[sqrt(x2 + y2)] + x + y = 4

A:

Q: 4. (a) Find dx (b) Using the result from part (a), evaluate. x So (1 + 22)3/2 (1+22)3/2 dx.

A: ANSWER : (a) ​  ANSWER : (b) ​

Q: Find the linear approximation to y=arcsinh(2x) at x=6.

A: Given:y=arcsinh(2x) and x0=6To find:The linear approximation to y=arcsinh(2x) at x0=6

Q: da Vx(1+ x) 1. 8.

A:

Q: Estimate I I≈ 27 - L² (3x 0 (3x - 1a²)da using midpoints and n = 3 subintervals.

A: In this question, we will find the integral by using mid-point method.

Q: d/dx (Vx)=1/vx.2 a. True b. False

A: using the differentiation  formula,       d/dx (xn )=nxn-1

Q: Consider the following: 25x squared +64y squared =1600 C) differentiate the explicit functions…

A:

Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.