Tafu is working with subatomic particles in the Physics lab. A positron is traveling in a straight line down the particle accelerator. Tafu models its position with the function +2 p(t)= t-1 where t>1. In the limit calculations below, if you need to use -co or co, enter -INFINITY or INFINITY. (a) Calculate the limit lim p(t) 0047 INFINITY (b) Calculate the limit lim p(t) t+1+ =INFINITY (c) Calculate the limit limp (t) t+2 4 (d) Let a>1 be some fixed number. Let h>0 be some small number. Write out a formula for the slope of the secant line to the graph of x=p(t) between the point at t=a and the point at t=a+h. You don't need to simplify this formula yet. (WARNING: When you write out an expression involving a and h, anytime you want to multiply a times h, you need to leave a single space between the two; i.e. "a h" means "a times h". In contrast, if you write "ah" the computer-web (e) Keep a fixed and think of your formula in (d) as a function in the variable h. Call it f(h). Now simplify your formula for f(h) so that it is a fraction with polynomials in the numerator and denominator, and the denominator does not var (WARNING: When you write out an expression involving a and h, anytime you want to multiply a times h, you need to leave a single space between the two; i.e. "a h" means "a times h". In contrast, if you write "ah" the computer=web (f) Calculate the limit limf (h) h→0 (g) A time t>1 when the positron's instantaneous velocity is zero is (h) Where is the positron located at the time you found in (g)