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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 or enter INFINITY or INFINITY a Calculate the limit lim p 0 11 b Calculate the limit lim p t 1 c Calculate the limit limp 1 1 2 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 ath 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 l e 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 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 L 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 I e 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 1 Calculate the limit lim h h 9 A time t I when the positron s Instantaneous velocity is zero is

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