Reference no: EM13167827

Evaluate the following limits using l'hopital's Rule
1) lim x->2 x^2-4x+4 / sin^2(πx)
2) lim x->0^+ x^2x
3)lim x->0 (x+cosx)^1/x
4)lim x->π/2^- (tanx-secx)

solution:
1)1/π^2
2)1
3)e
4)0

Mean Value Theorem

a. Determine whether the mean value Theorem applies to the following functions on the given interval [a,b]

b. If, so find or approximate the point(s) that are guaranteed to exist by the mean value theorem.

c. Make a sketch of the function and the line that passes through (a,f(a)) and (b,f(b)). Mark the points P (if they exist) at which the slope of the function equals the slope of the secant line. Then sketch the tangent line at P.

1)f(x)=arcsinx; [0,1/2]
Only parts a & b.
solution:
a) yes
b)c=√(1-9/πˆ2)

2)f(x)=x/(x+2); [-1,2]