Question

If f (2) = 1, \ f '(2) = - 3 and g (x) = log_2 (x ^ 2f (x) / cos (f (x)) then g' (2) is equal to: a)-9.625983

B)-3.327777

c)-4.800967

d)-12.01444

E)The answer doesn´t exist

Answer #1

does there exist a surface x=x(u,v) with E=1, F=0,
G=(cos^2)u and e=(cos^2)u, f=0, g=1 ?

Suppose that f(2) = −4, g(2) = 2, f '(2) = −5, and g'(2) =
1.
Find h'(2).
a. h(x)=2f(x)-5g(x)
h'(2)=?
b. h(x)=f(x)g(x)
h'(2)=?
c. h(x)=f(x)/g(x)
h'(2)=?
d. h(x)=g(x)/1+f(x)
h'(2)=?

a.)Consider the function f (x) = 3x/ x^2 +1
i) Evaluate f (x+1), and f (x)+1. Explain the difference. Do the
same for f (2x) and 2f (x).
ii) Sketch y = f (x) on the interval [−2, 2].
iii) Solve the equations f (x) = 1.2 and f (x) = 2. In each
case, if a solution does not exist, explain.
iv) What is the domain of f (x)?
b.)Let f (x) = √x −1 and g (x) =...

1. a True or False? If ∫ [ f ( x ) ⋅ g ( x ) ] d x = [ ∫ f ( x )
d x ] ⋅ [ ∫ g ( x ) d x ]. Justify your answer.
B. Find ∫ 0 π 4 sec 2 θ tan 2 θ + 1 d θ
C. Show that ∫ 0 π 2 sin 2 x d x = ∫ 0 π 2 cos...

1. If f(x) = ∫10/x t^3 dt then: f′(x)= ? and f′(6)= ?
2. If f(x)=∫x^2/1 t^3dt t then f′(x)= ?
3. If f(x)=∫x3/−4 sqrt(t^2+2)dt then f′(x)= ?
4. Use part I of the Fundamental Theorem of Calculus to find the
derivative of h(x)=∫sin(x)/−2 (cos(t^3)+t)dt. what is h′(x)= ?
5. Find the derivative of the following function:
F(x)=∫1/sqrt(x) s^2/ (1+ 5s^4) ds using the appropriate form of the
Fundamental Theorem of Calculus.
F′(x)= ?
6. Find the definitive integral: ∫8/5...

1)If f(x)=2x-2 and g(x)=3x+9, find the following. a)
f(g(x))=? b) g(f(x))=? c) f(f(x))=?
2)Let f(x)=x^2 and g(x)=6x-16. Find the following: a)
f(3)+g(3)=? b) f(3)*g(3)=? c) f(g(3))=? d) g(f(3))=?
3) For g(x)=x^2+3x+4, find and simplify
g(3+h)-g(3)=?
Please break down in detail. Please and Thank
you

a) Suppose that we have two functions, f (x) and g (x), and
that:
f(2)=3, g(2)=7, f′(2)=−4, g′(2)=6
Calculate the values of the following derivative when x is equal to
2: d ?x2 f (x)?|x=2
b) A spherical ice ball is melting, and its radius is decreasing
at a rate of 0.8 millimeters per minute. At what rate is the volume
of the ice cube decreasing when the radius of the sphere is equal
to 12 millimeters? Give your answer...

Suppose f(3) = 2 and f'(3) = −1.
a. If h(x) = x^2f(x), compute h'(3).
b. If k(x) = f(x)/x, compute k'(3).

Define g(x) = f(x) + tan-1 (2x) on [−1, √3/2 ].
Suppose that both f'' and g'' are continuous for all x-values on
[−1, √3/2 ]. Suppose that the only local extrema that f has on the
interval [−1, √3/2 ] is a local minimum at x = 1/2 .
(a) Determine the open intervals of increasing and decreasing
for g on the interval [1/2 , √3/2] .
(b) Suppose f(1/2) = 0 and f(√3/2) = 2. Find the absolute...

Let g (x) = [(x^2-3)/(x^3)]
(a) Determine (if they exist) the vertical and horizontal
asymptotes of g.
(b) Find the formula for g′ (x) and g′′ (x).
(c) Find (if they exist) the local extremes of g.
(d) Find (if they exist) the inflection points of g.
(e) Determine the intervals where g is increasing, and where g
is decreasing.
(f) Determine the intervals where g is concave upward, and
where g is
concave down.
(g) Plot the graph of...

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