1. Find the critical points, inflection points and asymptotes (if any) for the function f(x) = Determine the region where the function increase or decrease and also %3D x2-4 discuss it's concavity.
1. Find the critical points, inflection points and asymptotes (if any) for the function f(x) = Determine the region where the function increase or decrease and also %3D x2-4 discuss it's concavity.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Ques no. 1
![1. Find the critical points, inflection points and asymptotes (if any) for the function
f(x) = Determine the region where the function increase or decrease and also
discuss it's concavity.
%3D
2. Evaluate the following limits using L'Hopital's rule:
limx-b
and lim,(x-In(x5- 1010)].
xy
3. Let f(x,y) = r+yan (x,y)# (0,0)
(x, y) = (0,0)
where n > 1.
Discuss the continuity of f(x, y). And show that f(x,y) and fy(x, y) exist at all
points (x, y).
4. Find the equation of parabola which has axis parallel to y-axis and which passes
through the points (0, 2), (-1,0) and (1,6).
An ellipse circumscribes a rectangle whose sides are given by x =±2 and y = +4. If
the distance between the foci is 4V6 and major axis is along y-axis, then find the
equation of the ellipse.
%3D
= ue",
w = In(x2 +y2 +z?), x = ue" sin u, y = ue" cos u and z =
using chain rule at the point (u, v) = (-2,0).
5. If
find
aw
aw
and
av
du
6. Find the directions in which the function f (x, y, z) = In xy +In yz + In xz increase
and decrease most rapidly at the point Po(1,1,1). Then find the derivatives of the
function in those direetions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffa696cf4-7a69-48ae-8f9b-2ae407756ad6%2F45a56fc3-b081-4927-97e1-8ebfdebee084%2Fv2e7i8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Find the critical points, inflection points and asymptotes (if any) for the function
f(x) = Determine the region where the function increase or decrease and also
discuss it's concavity.
%3D
2. Evaluate the following limits using L'Hopital's rule:
limx-b
and lim,(x-In(x5- 1010)].
xy
3. Let f(x,y) = r+yan (x,y)# (0,0)
(x, y) = (0,0)
where n > 1.
Discuss the continuity of f(x, y). And show that f(x,y) and fy(x, y) exist at all
points (x, y).
4. Find the equation of parabola which has axis parallel to y-axis and which passes
through the points (0, 2), (-1,0) and (1,6).
An ellipse circumscribes a rectangle whose sides are given by x =±2 and y = +4. If
the distance between the foci is 4V6 and major axis is along y-axis, then find the
equation of the ellipse.
%3D
= ue",
w = In(x2 +y2 +z?), x = ue" sin u, y = ue" cos u and z =
using chain rule at the point (u, v) = (-2,0).
5. If
find
aw
aw
and
av
du
6. Find the directions in which the function f (x, y, z) = In xy +In yz + In xz increase
and decrease most rapidly at the point Po(1,1,1). Then find the derivatives of the
function in those direetions.
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