Use the Chain Rule and the fact that d (r)-L,o find the derivative of (b) Rewrite f(x) as a piecewise function not...
Using the Chain rule find the derivative of the function: 1. y=(x?+2x2,6
(Product Rule) Use the Product Rule to find the derivative of the function. f(x) = (4x+5)(x2 -8) O a. 2x + 4 Ob. 12x² + 10x - 32 O c. 8x O d. 8x2 – 40
Name: 1. For the function f(x) = x2 – 1 find and simplify: a. f(-2) b. f(-x) c. -f(x) d. f(x - 2) 2. Find the domain of each function below. Write your answer in interval notation. a. f(x) = x + 2 x2 + x - 6 b. 8(x) = (2x - 1 1 f(x + h) - f(x) 3. For the function f(x) = 2x2 – 3, find the difference quotient h 4. Use the graph of the...
4. Below is a piecewise function, determine -5 lim,f(x)= c, lim f(x)= e. lim f(x)- d. y = sin x (not drawn to scale) explain Consider the piece of f(x) in the first quadrant resembling e. Determine lim sinand the behavior of the graph near zero. 5. Using your graphing calculator sketch h(x)-x4-2x3 over [-2,2] below, find the critical values and on the graph label the coordinates of any local, global(absolute) minima, maxima or point of inflection on the sketch,...
a. Use the Chain Rule to find the indicated partial derivatives. z = x4 + x2y, x = s + 2t − u, y = stu2; ∂z ∂s ∂z ∂t ∂z ∂u when s = 1, t = 2, u = 3 b. Use the Chain Rule to find the indicated partial derivatives. w = xy + yz + zx, x = r cos(θ), y = r sin(θ), z = rθ; ∂w ∂r ∂w ∂θ when r = 8, θ = pi/2 c. Use the...
*PLEASE DO IN MATHEMATICA* {:1, ifr+ 13. Consider the function f(x)- nction,f(x)-e-r/rifx#0 a. Plot the graph of this function using Mathematica. b. Use the limit definition of the derivative and LHopital's Rule to show that every higher-order derivative of f at r 0 vanishes. c. Find the MacLaurin series for f. Does the series converge to f? {:1, ifr+ 13. Consider the function f(x)- nction,f(x)-e-r/rifx#0 a. Plot the graph of this function using Mathematica. b. Use the limit definition of...
For the piecewise linear function, find (a) f-3), (b) -2), (c) K0), (d) f(2), and (e) f(5) 2x ifxs-2 fix): x-2 ifx-2 (a) -3) (b) f-2)= (c) f(0)= (d) (2)= (e) 5)-
Find the directional derivative D−→ u f(x,y) of the function f(x,y) = x2 + 3xy + y3 where →− u is the unit vector given by angle θ = π 4. What is D−→ u f(1,1)?
Theorem 10.1.15 (Chain rule). Let X, Y be subsets of R, let xo e X be a limit point of X, and let yo e Y be a limit point of Y. Let f : X+Y be a function such that f(xo) = yo, and such that f is differentiable at Xo. Suppose that g:Y + R is a function which is differentiable at yo. Then the function gof:X + R is differentiable at xo, and .. (gºf)'(xo) = g'(yo)...
Q2) Find the derivative of each function a) f(1) = b) f(x) sin 1COSI 1+008 d) f(x) = (1 + x)'(1 - x)2 1 e) f(1) = 2009 1672 f). f() = ln(sec 0 + tan ) B): S(21) = 1n () h) y = (In(ax)? g(x) = ln(2.3 - 3x + 2) i) c) f(x) = sina