Ques no. 1 1. Find the critical points, inflection points and asymptotes (if any) for the functionf(x) = Determine the region where the function increase or decrease and alsodiscuss it's concavity.%3D2. Evaluate the following limits using L'Hopital's rule:limx-band lim,(x-In(x5- 1010)].xy3. 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 allpoints (x, y).4. Find the equation of parabola which has axis parallel to y-axis and which passesthrough the points (0, 2), (-1,0) and (1,6).An ellipse circumscribes a rectangle whose sides are given by x =±2 and y = +4. Ifthe distance between the foci is 4V6 and major axis is along y-axis, then find theequation 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. Iffindawawandavdu6. Find the directions in which the function f (x, y, z) = In xy +In yz + In xz increaseand decrease most rapidly at the point Po(1,1,1). Then find the derivatives of thefunction in those direetions.

Answered: Image /qna-images/answer/45a56fc3-b081-4927-97e1-8ebfdebee084.jpg

Answered: 1. Find the critical points, inflection…

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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Question

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.

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