Calculus Answers

The function sin(x) can be written as a Taylor series by:

Write a user-defined function file that calculates sin(x) by using the Taylor series. For the function name and arguments use y = Tsin(x,n). The input arguments are the angle x in degrees and n the number of terms in the series. Use the function to calculate sin(150 ) using R no of terms (where R is last digit of registation no; use 10 if last digit zero & use 11 if last digit is 1)

Given: x = 1 – cost and y = t – sint. Find y’.

Given: x = tan4t and y = sec4t. Find y’.

Give me two examples with solutions of each types of discontinuities

why will f(x)= x^2+7xz=10/x^3+7x^2+10x have at least one point discontinuity? THE SLASH IS THE FRACTION SYMBOL.. make the answer small, please.

Evaluate this integral x(x²+4)dx / x⁴+9

Given 𝑑𝑦

𝑑𝑥

= 𝑥 𝑥

2 + 𝑦

2

𝑒

−𝑥

and 𝑦(0) = 1, 𝑦(0.1) = 1.005, find

i) 𝑦 0.2 by Euler’s method

ii) 𝑦 0.3 by Modified Euler’s method

iii) 𝑦(0.4) by Milne’s predictor - corrector method.

If ux² + y² +2²,v=x+y+z₁w=xy+yz+zx, then the value of the jacobian is d(u,v,w)/d(x,y,z)

if f(x)=x² and g(x)=2x-1.find1.gf(x) 2.fg(x) 3.inverse of g(x)?

16 a Find the y-intercept of the tangent to f (x) = x In x at the point where: i x = 1 it x = 2 iii x = 3. b Make a conjecture about the y-intercept of the tangent to f (x) = x In x at the point where = a, a > 0. c Prove your conjecture algebraically. 17 Find the axes intercepts of the tangent to y = x2 ex at x = 1. 18 Find the exact area of the shaded triangle.