Hi can someone help me with these 5 questions?

Let A be a positive constant. Let f be a function such that f() = 5 and f' (It) = 2. If g(x) = In((f(x)) + A cosx), then g' (n) equals O 25 25 + A 25 O 10 25 - A O 20 25 - A O 1Letf be a function such that lin f(x) = 0. What is the value of , 1 11m f(x) cos( )? x>0 x O This limit does not exist. 00 Q There is not enough information given to determine whether or not this limit exists. Let f be a function which is continuous for all x with the following properties: f(-2) = -4, f(2) = 1, and lim f(x) = 0. X-+ 00 Which of the following assertions is always TRUE? Of (-2.5) = 1 There exists an A > 1 such that f(A) = 4000. There exists a c on the interval (-4, 1) such that f(c) = 0. There exists a c on the interval (-2, 2) such that f(c) = 2. There exists a c on the interval (-2, 2) such that f(c) = -1.Supposef is a continuous function defined on the interval [0, 3] and that some of its values are shown below, where k is a constant: Which of the following statements is always TRUE? 0 If k = 1, then the equationf(x) = 0 has at most one solution. Q If k = 2, then the equation f(x) = 0 has at least two solutions. Q If k = -1, then the equationf(x) = O has exactly two solutions. 0 If k = 1, then the equationf(x) = 0 has at least two solutions. Q If k = 2, then the equationf(x) = 0 has exactly two solutions. Let A be a positive constant. Let f be a function that is differentiable for all x. Suppose f(-1) = 3 and f'(-1) = 2. If g(x) = Af(x) e2x then g' (-1) equals 3A 2e2 3A + 2 (e2) 2 3A + 2e2 e4 O O-4A e2