Questions from General Calculus

Q: Find f'(x). Check that your answer is reasonable by

Find f'(x). Check that your answer is reasonable by comparing the graphs of f and f'. f (x) = √1 - x2 arcsin x

Q: Find f'(x). Check that your answer is reasonable by

Find f'(x). Check that your answer is reasonable by comparing the graphs of f and f'. f (x) = arctan (x2 -x)

Q: Find the limit. Limx→-1+ sin-1

Find the limit. Limx→-1+ sin-1 x

Q: Find the limit. limx→∞ arccos (1 + x2

Find the limit. limx→∞ arccos (1 + x2/1 + 2x2)

Q: Find the limit. limx→∞+ arctan (ex)

Find the limit. limx→∞+ arctan (ex)

Q: Find the exact value of each expression. (a).

Find the exact value of each expression. (a). tan-1 (tan3π/4) (b). cos (arccos ½)

Q: Find the limit. limx→0+ tan-1

Find the limit. limx→0+ tan-1 (ln x)

Q: If f and g are the functions whose graphs are shown,

If f and g are the functions whose graphs are shown, let u (x) = f (x) g (x) and v (x) = f (x) /g (x). (a). Find u'(1) (b). Find v'(5)

Q: (a). Suppose f is a one-to-one

(a). Suppose f is a one-to-one differentiable function and its inverse function f-1 is also differentiable. Use implicit differentiation to show that (f-1)'(x) = 1/f'(f-1(x)) provided that the denomin...

Q: (a). Show that f (x) = 2x +

(a). Show that f (x) = 2x + cos x is one-to-one. (b). What is the value of f-1(1)? (c). Use the formula from Exercise 41(a) to find (f-1)'(1). Exercise 41(a): (a). Suppose f is a one-to-one differen...