Sketch the function y = 8 + 10x − x^2 over the domain [0,7]. (a) If xA = 1,xB = 4, and λ = 0.4. Using the formula x′ =λxA (1 − λ)xB, determine the value of x′. What is the value of f(x′)? (b) Calculate the value of y′, which is the value of the secant line at x′, using the formula y′ = λf(xA) (1 − λ)f(xB). (c) Prove that the above function is strictly concave by demonstrating that f(x′) > y′.
Sketch the function y = 8 + 10x − x^2 over the domain [0,7]. (a) If...
Question For this problem, consider the function
y=f(x)=
|x|
+
x
3
on the domain of all real numbers.
(a) The value of
limx→
∞f(x)
is
. (If you need to use -∞ or ∞, enter -infinity or
infinity.)
(b) The value of
limx→
−∞f(x)
is
. (If you need to use -∞ or ∞, enter -infinity or
infinity.)
(c) There are two x-intercepts; list these in increasing
order: s=
, t=
.
(d) The intercepts in part (c) divide...
2. Find and sketch the domain of the function f(x,y) = V x2 – y + 2.
2. Find the average value of the function f(x,y) y 2. (Sketch the region.) 1/, y xy over the region bounded by y x, and
2. Find the average value of the function f(x,y) y 2. (Sketch the region.) 1/, y xy over the region bounded by y x, and
2 + (a) Determine and sketch the domain of the function f(x, y) = (x2 + y2 – 4) 9 – (x2 + y2). [7] x6 – yo (b) Evaluate lim (x,y)+(1,1) - Y [5] (c) What does it mean to say that a function f(x, y) has a relative minimum at (a,b)? [4] (d) Find all second order partial derivatives of the function f(x,y) = 22y.
calc3 #7
sketch by hand please
Find the domain of the function f(x,y) = In(x -y + 2) and sketch it in the xy-plane.
For the function g(x)= 10x² + 9x Express the slope of the secant line in terms of x and h. Find m e for h=0.5, 0.1, and 0.01 at x 1. What value does m approach as h approaches 0? (c) Find the equation for the secant line at x 1 with h -0.01. Graph g and the secant line found in part (c) on the same viewing window Find the average rate of change of f(x) x - 2x...
ID Let f(x) = /2x=2 | (a) Find f'(x) as a piecewise function (6) Graph y = f'(x) (c) state the domain of f and the domain of f. Find lin tan 4x cos 3x sin 5x X> 12 Find y if y = (3x+5)*(x+4x) (3 Find y' it ya + 10x tanx 7 Let y= (a) Find (6) Find the equation of the tangent line at (74 y' Elf 8 X3 Prove lim (5-) = 4 (a) write the...
5) Given the function fix.y) - x2 and region R bounded by x 0, y x and 2x+y 6 (a) Sketch the region R (label lines, intercepts, axes and shade region) (b) SET UP the integral over this region (c) Assuming f(x.y)- xa is the density function for the lamina R given above, determine the mass for R
5) Given the function fix.y) - x2 and region R bounded by x 0, y x and 2x+y 6 (a) Sketch the...
QUESTION 5 a) Find and sketch the domain of the function f(x,y) = \n(x2 - y +1) + VÝ +1. (5 marks) b) Evaluate eży sin(3x +2y) lim (x,y) (-2,3) 3x +2y (6 marks)
6. Consider the function f(x) = x3 - 10x (a) (3 pts) Find f '(x) (b) (9 pts.) Find the intervals where f(x) is increasing/decreasing, and classify any local max/min. (c) (3 pts) Find f '(x) (d) (9 pts.) Find the intervals where f(x) is concave up/down and classify any inflection points. Using the information from parts a-d only, sketch the graph of y=f(x).