# math7 - Practice problems for midterm 2 1 Find the first...

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Unformatted text preview: Practice problems for midterm 2 1. Find the first and second derivative of (a) f ( x ) = √ x + 1 3 √ x 2 (b) f ( x ) = x +1 x 3 + x- 2 (c) f ( x ) = sin x cos x +7 (d) f ( x ) = x 7 sin x tan x (e) f ( x ) = p x + √ x (f) f ( x ) = 3 √ 1 + tan x (g) f ( x ) = e x cos x (h) f ( x ) = sin(tan x ) (i) f ( x ) = sin- 1 (2 x + 1) (j) f ( x ) = ln( x √ x- 1) (k) f ( x ) = cosh(ln x ) (l) f ( x ) = x sinh x- cosh x 2. Use implicit differentiation to compute dy dx . (a) x 3 + y 3 = 1 (b) √ x + y = 1 + xry 2 (c) 4 cos x sin y = 1 (d) 1 + x = sin( xy 2 ) (e) e y cos x = 1 + sin( xy ) 3. Find the limit of (a) lim x → sin 4 x sin 6 x (b) lim t → sin 2 3 t t 2 (c) lim θ → cos θ- 1 sin θ 4. Use logarithmic differentiation to find dy dx . (a) y = (2 x + 1) 5 ( x 4- 3) 6 (b) y = 4 q x 2 +1 x 2- 1 (c) y = (sin x ) ln x (d) y = (tan x ) 1 /x 5. A bacteria culture grows at a rate proportional to its size. After 2 hours there are 600 bacteria and after 8 hours the count is 75 , 000....
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math7 - Practice problems for midterm 2 1 Find the first...

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