1 Consider the function f(x) x+1 1 (a) Evaluate lim x>0 x +1 (b) Find the stationary point of the curve y = f(x) and determine its nature. (c) Find the point(s) of inflection of the curve y = f(x) . (d) Sketch the curve y = f(x) showing all the features found above. Using your graph, find all values of k for which the equation kx? =1-k has exactly one solution. (e)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
(ii)
1
Consider the function f(x)=
x* +1
(a)
1
Evaluate lim
x>0 x + 1
(b)
Find the stationary point of the curve y = f(x) and determine its nature.
(c)
Find the point(s) of inflection of the curve y = f(x) .
(d)
Sketch the curve y = f(x) showing all the features found above.
Using your graph, find all values of k for which the equation kx? = 1-k has
exactly one solution.
(e)
Transcribed Image Text:(ii) 1 Consider the function f(x)= x* +1 (a) 1 Evaluate lim x>0 x + 1 (b) Find the stationary point of the curve y = f(x) and determine its nature. (c) Find the point(s) of inflection of the curve y = f(x) . (d) Sketch the curve y = f(x) showing all the features found above. Using your graph, find all values of k for which the equation kx? = 1-k has exactly one solution. (e)
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