Midterm Practice Questions - MATHEMATICS 115 MIDTERM...

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MATHEMATICS 115 MIDTERM PRACTICE PROBLEMS 1. Find y .
2. Evaluate the following limits. (a) lim x 0 + sin x ln x (b) lim x 0 2 sin x - sin 2 x 2 e x - 2 - 2 x - x 2 (c) lim x →∞ ( e x + 1) 1 x (d) lim x →∞ x [ln(2 + 3 x ) - ln(3 x - 1)] (e) lim x →∞ parenleftBig 1 + r x parenrightBig ax , a, r constants (f) lim x 1 parenleftbigg x x - 1 - 1 ln x parenrightbigg (g) lim x →∞ cosh 2 x e 3 x - e 3 x 3. (a) Solve for x given that ln( x - 3) + ln( x + 6) = ln 5 + ln 2 . (b) Solve for t given that y = 7 e (5ln2) t . (c) Simplify sin ( tan 1 x x 2 +1 ) . (d) Let f ( x ) = e x + ln x . Show that f 1 exists and find ( f 1 ) ( e ) using the formula derived in class. (e) Find the average value of the function f ( x ) = x 2 3 - x on [0 , 2] .

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