The squeeze theorem - Study guides, Class notes & Summaries

Squeeze Theorem f is continuous at x=c if... Intermediate Value TheoremIf f is continuous on [a,b] and k is a number between f(a) and f(b), then there exists at least one number c such that f(c)=k Global Definition of a Derivative Alternative Definition of a Derivativef '(x) is the limit of the following difference quotient as x approaches c

Jump Discontinuity - ANSWERWhen the two-sided limit doesn't exist because the one-sided limits aren't equal. Infinite Discontinuity - ANSWERWhen the two-sided limit doesn't exist because it's unbounded. Removable Discontinuity - ANSWERWhen the two-sided limit exists, but isn't equal to the function's value. Squeeze Theorem - ANSWERƒ(x) ≤ g(x) ≤ h(x) for all x and if the limit of ƒ(x) as x→c = L and the limit of h(x) as x→c = L, then the limit of g(x) as x→c...

limit of one/both functions are DNE - ANS evaluate the limit from the left and the right hand of the approaching value values match = limit exists squeeze theorem - ANS f(x) < h(x) < g(x) limit of f(x) = limit of g(x) = # by squeeze theorem limit of h(x) = # removeable discontinuity - ANS limit does not equal the point jump discontinuity - ANS limit from the left does not equal the limit from the right infinite discontinuity - ANS li...

Squeeze Theorem - ANSWERIf h(x) ≤ ƒ(x) ≤ g(x) for all x in an open interval containing c, except possibly at c itself, and lim x→c h(x) = lim x→c g(x) = L, then lim x→c ƒ(x) exists and equals L. Continuity - ANSWERA function ƒ is continuous at c if: a. ƒ(c) is defined b. lim x→c ƒ(x) exists c. lim x→c ƒ(x) = ƒ(c) Intermediate Value Theorem - ANSWERIf ƒ is continuous on an interval [a,b] and k is any number between ƒ(a) and ƒ(b), there is at least one number c in ...

AP Calculus BC Exam Review Questions with Correct Answers | Graded A+ Jump Discontinuity - When the two-sided limit doesn't exist because the one-sided limits aren't equal. Infinite Discontinuity - When the two-sided limit doesn't exist because it's unbounded. Removable Discontinuity - When the two-sided limit exists, but isn't equal to the function's value. Squeeze Theorem - ƒ(x) ≤ g(x) ≤ h(x) for all x and if the limit of ƒ(x) as x→c = L and the limit of...

taking a continuous object and breaking it up to approximate (advantages, disadvantages) - ANSWERdisadvantage- more pieces to deal with advantage- more accurate estimate Calculus - ANSWERall about limits and the attempt of closing in on an exact value of an answer by using finer and finer approximations limit - ANSWERthe idea of a limit is that we are attempting to see what the output (y) approaches, if anything, as the input (x) approaches a particular value limit (L) can be one of fo...

Function - correct answer A rule that assigns "x" exactly one element called f(x). Lines - correct answer y=mx+b m=(y2-y1)/(x2-x1) Polynomial - correct answer A monomial or a sum or difference of monomials Rational Function - correct answer a ratio of polynomials Power Function - correct answer y...

AP Calculus BC All of the theorems and rules you will need to know for the Calculus BC test. If h(x) ≤ ƒ(x) ≤ g(x) for all x in an open interval containing c, except possibly at c itself, and lim x→c h(x) = lim x→c g(x) = L, then lim x→c ƒ(x) exists and equals L. - Answer>>Squeeze Theorem A function ƒ is continuous at c if: a. ƒ(c) is defined b. lim x→c ƒ(x) exists c. lim x→c ƒ(x) = ƒ(c) - Answer>>Continuity

Secant Line Correct Answer The line connecting any two points on a curve. Tangent Line Correct Answer The line that best approximates a function near a point A. It's the limit of secant lines connecting points A & B as B approaches A. Squeeze Theorem Correct Answer If f(x)≤g(x)≤h(x) and if the top and bottom functions both have the same limits, we can conclude that the middle function must have the same limit. Continuity Correct Answer A function, f, is continuous at x=a if the lim...

AP Calculus AB Theorems ƒ(x) ≤ g(x) ≤ h(x) for all x and if the limit of ƒ(x) as x→c = L and the limit of h(x) as x→c = L, then the limit of g(x) as x→c = L - Answer-Squeeze Theorem If ƒ is continuous on [a,b] and k is a value between ƒ(a) and ƒ(b), then there is at least one c in [a,b] such that ƒ(c) = k - Answer-Intermediate Value Theorem If ƒ(x) is continuous on [a,b], then ƒ(x) has a max and a min - Answer-Extreme Value Theorem The absolue extrema of a function ...