Calculus AB Educational Learning Objectives Science Academy
... • Evaluate trigonometric functions using special triangles and the unit circle • Graph the basic trigonometric functions • Solve trigonometric equations • Fit linear, quadratic and trigonometric models to real-life data sets ...
... • Evaluate trigonometric functions using special triangles and the unit circle • Graph the basic trigonometric functions • Solve trigonometric equations • Fit linear, quadratic and trigonometric models to real-life data sets ...
Computing Indefinite Integrals
... 7. Have each table come up with the antiderivative formulas for all the trig functions by reversing the derivative formulas. 8. Have them work on figuring out the antiderivative formulas for ex, ax, and ln(x). Explain how the ln(x) fills in the hole from before where x = -1. 9. Teach the students ho ...
... 7. Have each table come up with the antiderivative formulas for all the trig functions by reversing the derivative formulas. 8. Have them work on figuring out the antiderivative formulas for ex, ax, and ln(x). Explain how the ln(x) fills in the hole from before where x = -1. 9. Teach the students ho ...
Math 171 Final Exam Review: Things to Know
... − Find critical points. − Extreme Value Theorem (page 238) − Know how to locate absolute extrema on a closed interval. (See page 241) • Test for Intervals of Increase and Decrease (page 246) • First Derivative Test (page 249) • Concavity and Inflection Points − See the test for concavity on page 252 ...
... − Find critical points. − Extreme Value Theorem (page 238) − Know how to locate absolute extrema on a closed interval. (See page 241) • Test for Intervals of Increase and Decrease (page 246) • First Derivative Test (page 249) • Concavity and Inflection Points − See the test for concavity on page 252 ...
1 Distributions or generalized functions.
... We can translate the Heaviside distribution at x0 and usually people write H(x − x0 ) to indicate such a translation. A rectangular pulse of magnitude a of duration t is given by a function whose value is a in an interval of length t. Such rectangular pulse Ra,t (x) can be obtained by using the Heav ...
... We can translate the Heaviside distribution at x0 and usually people write H(x − x0 ) to indicate such a translation. A rectangular pulse of magnitude a of duration t is given by a function whose value is a in an interval of length t. Such rectangular pulse Ra,t (x) can be obtained by using the Heav ...
7.2 Partial Derivatives
... to y at the point (a, b) and is usually denoted by ∂f ∂y (a, b) or fy (a, b). If the function f (x, y) is given by a formula, then the values fx (a, b) and fy (a, b) are very easy to compute. In order to find fx (a, b) we consider the function f (x, b) of ONE variable x and simply differentiate this ...
... to y at the point (a, b) and is usually denoted by ∂f ∂y (a, b) or fy (a, b). If the function f (x, y) is given by a formula, then the values fx (a, b) and fy (a, b) are very easy to compute. In order to find fx (a, b) we consider the function f (x, b) of ONE variable x and simply differentiate this ...
Fixed Point Theorems, supplementary notes APPM
... let D ⊂ H for a Hilbert space H, and consider a function T : D → H. We say T is firmly non expansive if for all x, y ∈ D, kT (x) − T (y)k2 + k(I − T )(x) − (I − T )(y)k2 ≤ kx − yk2 . Here, we use I to denote the identity mapping. Then the following are equivalent: (a) T is firmly nonexpansive (b) I ...
... let D ⊂ H for a Hilbert space H, and consider a function T : D → H. We say T is firmly non expansive if for all x, y ∈ D, kT (x) − T (y)k2 + k(I − T )(x) − (I − T )(y)k2 ≤ kx − yk2 . Here, we use I to denote the identity mapping. Then the following are equivalent: (a) T is firmly nonexpansive (b) I ...
A function f is linear if f(ax + by) = af(x) + bf(y) Or equivalently f is
... Some algebra implies L(y) = ...
... Some algebra implies L(y) = ...
Chapter 1
... Use the Intermediate Value Theorem to show that the polynomial function f (x) = x 3 + 2x -1 has a zero in the interval [0, 1]. First Note that f is continuous on the closed interval [0, 1]. Then plug in the endpoints into the function. Since the function goes from negative to positive, ZERO has to e ...
... Use the Intermediate Value Theorem to show that the polynomial function f (x) = x 3 + 2x -1 has a zero in the interval [0, 1]. First Note that f is continuous on the closed interval [0, 1]. Then plug in the endpoints into the function. Since the function goes from negative to positive, ZERO has to e ...
Document
... line segment will be integrand f(x) - g(x) Step 3 Determine the limits. The left at which the line segment intersects the region is x=a and the right most is x=b. ...
... line segment will be integrand f(x) - g(x) Step 3 Determine the limits. The left at which the line segment intersects the region is x=a and the right most is x=b. ...
