Calculus Terms Exam Questions and Answers Latest Update 2024 (Already Passed)

Calculus Terms Exam Questions and Answers Latest Update 2024 (Already Passed) What is the definition of a tangent line? - Answers A line that touches a curve at one point What is the definition of a secant line? - Answers A line that touches a curve at two points What is the definition of a point of tangency? - Answers The point where the tangent line touches a curve What is the difference between average and instantaneous rate of change? - Answers Instantaneous is the rate at a specific moment. Average is the rate over a time interval. How do you find an average rate of change? - Answers The slope of the secant How do you approximate an instantaneous rate of change? - Answers Choose two points close to the specified value and find the slope between them When will a limit exist at k=n? - Answers When the limit from the left equals the limit from the right How do we find a limit? - Answers Substitute, graph, approximate or algebra How do you find a horizontal asymptote? - Answers Find the limit as x approaches positive and/or negative infinity How do we know if y=b is a horizontal asymptote? (technical definition) - Answers lim f(x)=b x->infinity lim f(x)=b x->-infinity How do we know if x=a is a vertical asymptote? (technical definition) - Answers lim f(x)=+-infinity x->a+ lim f(x)=+-infinity x->a- How do we find an end behavior model for rational functions? - Answers Determine which part of the function has more "power" at endpoints and use that How do you prove a function is continuous at x=a? - Answers limit at a = the value at a Define the Intermediate Value Theorem? - Answers If f(x) is continuous, then every value between f(a) and f(b) must exist How do we find the slope of a function at x? - Answers lim f(x+h)-f(x)/h h->0 What is the formula for finding the slope of a curve at a point? - Answers lim f(x+h)-f(x)/h h->0 What is a normal line? - Answers A line perpendicular to a tangent line Where will a derivative not exist? - Answers corner, cusp, vertical tangent, discontinuity If a function is differentiable, will it be continuous? - Answers Yes If a function is continuous, will it be differentiable? - Answers maybe What is the intermediate value theorem for derivatives? - Answers If a function is continuous, then the derivative must take on all values between f(a) and f(b) What formula should I remember for the product rule? - Answers uphill+downhill What formula should I remember for the quotient? - Answers (uphill-downhill) divided by the denominator squared For derivatives, how will you know when to use the product rule? - Answers When two or more functions are multiplied For derivatives, how will you know when to use the quotient rule? - Answers When two or more functions are divided