Calculus show work please

Problem 1. The point P(4,2) lies on the curve y =vx a) The point Q (x, vx ) is also on the graph. Find the slope of the secant line PO(correct to 4 decimal places) for the following x value: (3 pts.) 1) 1 ii)3 iiijs b) Use the results of part (a) to estimate the slope of the tangent line to the graph of fat P(4,2). Describe how to improve your approximation of the slope. (2 pts.) Problem 2. Let f(x) =_;, Guess the value of lim f(x) by evaluating the function at the given X-4 numbers (correct to 5 decimal places) (6 pts.) x=3.9, 3.99, 3.999, 4.001, 4.01, 4.1 Problem 3. Determine the infinite limit (2 pts.) X 5 lim x-2 (2 - *)2 Problem 4. Find the limit 5 -Vr a) lim = 25 (3 pts.) -25 b) lim 15- (3 pts.)