6 78 points previous answers tafu is working with

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6. 7/8 points | Previous Answers 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)= t 2 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_(t­>infty) p(t)= infinity . (b) Calculate the limit lim_(t­>1^+) p(t)= infinity . (c) Calculate the limit lim_(t­>2) p(t)= $$4 . (d) Let a>1 be some fixed number. Let h>0 be some small number. Write out a formula for the slope of the secant line to the graph of x=p(t) between the point at t=a and the point at t=a+h . You don't need to simplify this formula yet. (WARNING: When you write out an expression involving a and h , anytime you want to multiply a times h , you need to leave a single space between the two; i.e. " a h " means " a times h ". In contrast, if you write " ah " the computer=webassign thinks that you are talking about a new variable called " ah ". Alternatively, use the arithmetic buttons in the pop­up box whenever you want to add, subtract, multiply or divide.): $$( a + h )2 a + h −1− a 2 a −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; i.e. " a h " means " a times h ". In
6/5/2019 hw07S2.7-8 7/10 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 pop­up box whenever you want to add, subtract, multiply or divide.): $$ a 2− ah −2 a h ( a + h −1)( a −1) (f) Calculate the limit lim_(h­>0) f(h)= $$ a 2−2 a ( a −1)2 (g) A time t>1

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