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

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

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...

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...

QUESTION 1 (a) Determine the following limits (if they exist): (i) (3) (ii) x  2 lim 3  x 1 2 (3) x 3 x  9 (iii) (iv) lim x  2x lim 1  x (3) (3) (v) x  1 lim 1  x 2x (3) (vi) lim sin t  tan 2t (3) t  0 t (b) Use the Squeeze Theorem to determine the following limit: 5k 2  cos3k lim 2 . (3) ...

MAT1512 EXAM PACK 2023 LATEST QUESTIONS AND ANSWERS 1 [TURN OVER] 2 x 0 3  x  9 x2  x  QUESTION 1 (a) Determine the following limits (if they exist): (i) (3) (ii) x  2 lim 3  x 1 2 (3) x 3 x  9 (iii) (iv) lim x  2x lim 1  x (3) (3) (v) x  1 lim 1  x 2x (3) (vi) lim sin t  tan 2t (3) t  0 t (b) Use the Squeeze Theorem to determine the following limit: 5k 2  cos3k lim 2 . (3)  x  ...

MAT1512 EXAM PACK 2023 LATEST QUESTIONS AND ANSWERS 1 [TURN OVER] 2 x 0 3  x  9 x2  x  QUESTION 1 (a) Determine the following limits (if they exist): (i) (3) (ii) x  2 lim 3  x 1 2 (3) x 3 x  9 (iii) (iv) lim x  2x lim 1  x (3) (3) (v) x  1 lim 1  x 2x (3) (vi) lim sin t  tan 2t (3) t  0 t (b) Use the Squeeze Theorem to determine the following limit: 5k 2  cos3k lim 2 . (3)  x  ...

AP Calculus AB 2023 1 - 0 - Squeeze Theorem - f is continuous at x=c if... - Intermediate Value Theorem - If 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 Derivative - f '(x) is the limit of the following difference quotient as x approaches c nx^(n-1) - 1 - cf'(x) - f'(x)+g'(x) - f'(x)-g'(x) - cos(x) - -sin(x)...

a) Determine the following limits (if they exist): (i) 3 1 6 2 lim 2      x x x (3) (ii) 3 9 lim 2 3      x x x (3) (iii) x x x x x 2 4 2 lim 2     (3) (iv) xx x    1 1 lim 1 (3) (v) 3 9 2 lim  0  x  x x (3) (vi) t t t t sin tan 2 lim 0   (3) (b) Use the Squeeze Theorem to determine the following limit: . 10 5 cos3 lim 2 2     k k k k (3) (c) ...

a) Determine the following limits (if they exist): (i) 3 1 6 2 lim 2      x x x (3) (ii) 3 9 lim 2 3      x x x (3) (iii) x x x x x 2 4 2 lim 2     (3) (iv) xx x    1 1 lim 1 (3) (v) 3 9 2 lim  0  x  x x (3) (vi) t t t t sin tan 2 lim 0   (3) (b) Use the Squeeze Theorem to determine the following limit: . 10 5 cos3 lim 2 2     k k k k (3) (c) ...