Im not really sure how to do some questions....
1. Find lim(x-> 0) [sin(6x+pi/6) - sin(pi/6)]/x, if it exists
What I did was separate the numerator into sin(x) +sin(pi/6) - sin(pi/6). Since sin(pi/6) is equal to 1/2, they cancel out and it leaves to sin(x)/x, and this would = 1, not sure if I did it right or not...
2. Given a thrice-differentiable function f(x), its Maclaurin polynomial of degree 3 is the polynomial of the form
g(x) = a0 + a1x + a2x^2 + a3x^3
(the 0, 1, 2, and 3, are subscript)
satisfying the conditions g(0) = f(0), g'(0) = f'(0), g''(0) = f''(0) and g^(3) (0) = f^(3) (0). Find the Maclaurin polynomials of degree 3 for the following functions:
a. f(x) = sinx
b. f(x) = cosx
c. f(x) = e^x