Calculus Exam 1 – Practice Questions with Complete Solutions

Ohio State University-Main Campus MATH 1151



CALCULUS EXAM 1 QUESTIONS WITH COMPLETE SOLUTIONS



Function relationship that for every input there is only one output


Vertical Line Test exactly one output


Horizontal Line Test different inputs never yield same output


Inverse function undoes whatever original function did


Limits as the input x goes very close to but not equal to a, does f(x) get very close to L?;
the value f wants to be at x = a


one-sided limits x approaches a from only one side instead of both sides


the limit exists if and only if _________ both one-sided limits exist and are equal


Continuity f is continuous at x=a if the limit as x approaches a of f(x) equals f(a); f(a) is defined,
and the limit as x approaches a of f(x) exists; can we draw graph without lifting
pencil?


One-sided continuity f is continuous from one side if the limit as x approaches a equals f(a)


intervals of continuity (a,b) f continuous for all c in (a,b)


intervals of continuity [a,b) f is right continuous at x=a


intervals of continuity (a,b] f is left continuous at x=b


intervals of continuity [a,b] f is left and right continuous at x=a and x=b


Basic functions continuous on their domains X^n, trig functions, arc-trig functions, exponential functions, log functions, and
constants (sometimes polynomials and rational functions)


Squeeze Theorem Suppose g(x) is less than or equal to f(x) is less than or equal to h(x) for all x
near a, and suppose L = the limit as x approaches a of g(x) = the limit as x
approaches a of h(x). Then the limit as x approaches a of f(x) = L


form of a limit what we get by trying to plug in


indeterminant form a form that doesn't properly evaluate to a number


Ways to deal with 0/0 factor and cancel; multiply top and bottom by conjugate


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