MAC-2311 Midterm: MAC 2311-17 test-3-key
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You may use the back of a page if you need more space for a problem. Page 2 of 8: (4 points) find the di erential of the function given by f (x) = x3/4. 4: (10 points) find the derivative of the function given by f (x) = cosh(x) tanh 1( x). (hint: the derivative of tanh 1 at x is. Solution: f (x) = sinh(x) tanh 1( x) + cosh(x) Page 3 of 8: in each part, nd the limit if it exists. If the limit is not nite, write or (depending on its sign). If the limit otherwise does not exist, write dne and explain why. (a) (4 points) sinh(x) lim x . Solution: lim x sinh(x) = lim x ex e x. If it did, sin(x) would horizontally asymp- tote to a line as x . But sin has no horizontal asymptote. (c) (8 points) lim x x2e x.
