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 p(t)= i t- 1 where t>1. In the limit calculations below, if you need to use -ec or 00, enter -INFINITY or INFINITY. (a) Calculate the limit 1' t c.1330" I: INFINITY q (b) Calculate the limit Iim t lql+p( )= INFINITY J (c) Calculate the limit 3'32""): 4 V (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; Le. "a h" means "a times h". In contrast, if you write "ah" the computer=webassign thinks that you are talking about a new variable called "ah". Alternatively, use the arithmetic buttons in the pop-up box whenever you want to add, subtract, multiply or divide.): (a+h)2 _ a+h—1 h

(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 vanish at h=0; i.e. your final answer should be a rational function in h which is defined at h=0. (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; Le. "a h" means "a times h". In contrast, if you write "ah" the computer=webassign thinks that you are talking about a new variable called "ah". Alternatively, use the arithmetic buttons in the pop-up box whenever you want to add, subtract, multiply or divide): (f) Calculate the limit lim f (h) h—m = (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)