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Calculus
The equation of the tangent plane to h(x,y)=yln(x) at the point (1,5) is
Select one:
a. z=1/5x+1/5y
b. z=x+y
c. z=1/4x+1/4y
d. z=4(x−1)
e. z=5(x+1)
f. z=5(x−1)
Select one:
a. z=1/5x+1/5y
b. z=x+y
c. z=1/4x+1/4y
d. z=4(x−1)
e. z=5(x+1)
f. z=5(x−1)
Calculus
Answer the following questions for the function
f(x)=x3x2−36
defined on the interval [−15,15].
a.) Enter the x-coordinates of the vertical asymptotes of f(x) as a comma-separated list. That is, if there is just one value, give it; if there are more than one, enter them separated commas; and if there are none, enter NONE .
Answer:
-6,6
b.) f(x) is concave up on the region
(-6,0)U(6,18)
Note: Give your answer in interval notation.
c.) Enter the x-coordinates of the inflection point(s) for this function as a comma-separated list.
Answer:
Calculus
Check whether these statements are sets or not give reason for your answer.
(I) The collection of all rectangles that are not squares.
(ii) The Asiatic Society library collection
(I) The collection of all rectangles that are not squares.
(ii) The Asiatic Society library collection
Calculus
The equation of the tangent plane to h(x,y)=yln(x) at the point (1,5) is
Select one:
a. z=1/5x+1/5y
b. z=x+y
c. z=1/4x+1/4y
d. z=4(x−1)
e. z=5(x+1)
f. z=5(x−1)
Select one:
a. z=1/5x+1/5y
b. z=x+y
c. z=1/4x+1/4y
d. z=4(x−1)
e. z=5(x+1)
f. z=5(x−1)
Calculus
Let f(x,y) be a function of x and y. The partial derivative of f(x,y) with respect to y is equivalent to the directional derivative of f(x,y)
in the direction of the unit vector
Select one:
a. ⟨1,0⟩
b. ⟨1,1,1⟩
c. ⟨0,5⟩
d. ⟨0,1⟩
in the direction of the unit vector
Select one:
a. ⟨1,0⟩
b. ⟨1,1,1⟩
c. ⟨0,5⟩
d. ⟨0,1⟩
Calculus
Let f
be a function of two variables. Which of the following statements is true?
Select one:
a. If (a,b)
is a critical point of f, then f has a local maximum at (a,b)
.
b. f
must have a saddle point.
c. If f
has a local maximum at (a,b), then (a,b)
is a critical point.
d. If (a,b)
is a critical point of f, then f has a local minimum at (a,b).
be a function of two variables. Which of the following statements is true?
Select one:
a. If (a,b)
is a critical point of f, then f has a local maximum at (a,b)
.
b. f
must have a saddle point.
c. If f
has a local maximum at (a,b), then (a,b)
is a critical point.
d. If (a,b)
is a critical point of f, then f has a local minimum at (a,b).
Calculus
Let f(x,y)∈R be a function of two variables. Then the gradient of f
is
Select one:
a. equal to the directional derivative of f
b. a vector in R2
c. a vector in R3
d. a scalar
is
Select one:
a. equal to the directional derivative of f
b. a vector in R2
c. a vector in R3
d. a scalar
Calculus
Let f be a function of ten variables. Then f
has
Select one:
a. no third order partial derivatives.
b. twenty second order partial derivatives.
c. no first order partial derivatives.
d. ten first order partial derivatives.
has
Select one:
a. no third order partial derivatives.
b. twenty second order partial derivatives.
c. no first order partial derivatives.
d. ten first order partial derivatives.
Calculus
Let f(x,y)=x^3+y^3−12xy, then, Select one:
a. f has a local maximum at (4,4)
b. f has a local minimum at (0,0)
c. f has a saddle at (0,0)
d. f has a saddle at (4,4)
a. f has a local maximum at (4,4)
b. f has a local minimum at (0,0)
c. f has a saddle at (0,0)
d. f has a saddle at (4,4)
Calculus
Find the area of the region enclosed enclosed between the graphs of y=e^x and y=e^-x and the line x=ln2.
