Estimate the area under the graph of f(x)=1/(x+4) over the
interval [-1,2] using five approximating rectangles and
right endpoints.
Rn=
Repeat the approximation using left endpoints.
Ln=
Estimate the area under the graph of
f(x)=25−x^2
from x=0 to x=5 using 5 approximating rectangles and right
endpoints.
(B) Repeat part (A) using left endpoints.
(C) Repeat part (A) using midpoints.
Approximate the area under the graph of f(x) and above the
x-axis with rectangles, using the following methods with
n=4.
f(x)=88x+55
from
x=44
to
x=66
a.
Use left endpoints.
b.
Use right endpoints.
c.
Average the answers in parts a and b.
d.
Use midpoints.
Given f(x) = 1 x 2 − 1 , f 0 (x) = −2x (x 2 − 1)2 and f 00(x) =
2(3x 2 + 1) (x 2 − 1)3 . (a) [2 marks] Find the x-intercept and the
y-intercept of f, if any. (b) [3 marks] Find the horizontal and
vertical asymptotes for the graph of y = f(x). (c) [4 marks]
Determine the intervals where f is increasing, decreasing, and find
the point(s) of relative extrema, if any....
6) Given: (a) f (x) = (2x^2)/(x^2 −1) - Calculate f ′(x) and f
″(x) - Determine any symmetry - Find the x- and y-intercepts - Use
lim f (x) x→−∞ and lim f (x) x→+∞ to determine the end behavior -
Locate any vertical asymptotes - Locate any horizontal asymptotes -
Find all intervals where f (x) is increasing and decreasing - Find
the open intervals where f (x) is concave up or concave down
the figure shows the graph of f(x) =
ex. in the exercise 1 to 4, use
transformation of this graph to graph each function. be sure to
give equation of this the asymptotes. use the graph to determine
each function's domain and range. if applicable, use a graphing
utility to confirm your graph
1). g(x) = ex-1
2). g(x) = ex+2
3) h(x) = e-x
4) g(x) = 2ex
Let f(x)=(x^2+1)*(2x-3)
Find the equation of the line tangent to the graph of f(x) at
x=3.
Find the value(s) of x where the tangent line is horizontal.
1:
Given that f(4) = 6 and f'(x) = 2/x2+9 for all x.
a) Use a linear approximation or differentials to estimate
f(4.04)
b) Is your estimate in part (a) too large or too small?
Explain.
2:
a) Given f(x) = (x + 3)sinx, find f'(π) using
logarithmic differentiation.
b) Find the value of h'(0) if h(x)+xsin(h(x))=
x2+4x-π/2