Calculus Answers

Determine the radius of a circle whose arc length measures meters and central angle measures radians. Round your answer to the nearest hundredth.

r = meters

Can we apply L’ Hospital’s rule to evaluate the limit, 2 3 2
5
x
x cos x lim
x→∞ +
? Justify.

Find the point on the terminal side of θ = negative three pi divided by four that has an x coordinate of -1.

The point P(21, 28) is on the terminal side of θ. Evaluate sin θ.

Obtain the Fourier cosine series for the following function:


F(x)= 1 for (0 less than equal to x< 1)

0 for (1 less than equal to x < 4 )

Find the limit of

Lim (x+3)^2-9
----------------
2x
X----->0

Find the rate of change of h(x)=2 cos⁡〖(3x+tan⁡x)〗 with respect to x.

Choose the correct answer.
Q.The eigen values of the matrix ■(0&a@-2&-3) are a-3 and -1. Find a.
a. a=-1
b. a=1
c. a=0
d. a=2

Q.Which of following function is analytic in comolex plane.
(i) f(z)=z ̅ (ii) f(z)=2x+ixy^2 (iii) f(z)= z^2

Q. If f(x)= ∑_(n=0)^∞▒n^(n⁄2)/n! x^(n ), then f^6(0)=?