Question
Asked Sep 25, 2019
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(kax if x<2
f(x)=11- kx if 2s x
Consider the piecewise function:
6.
Find values of the constants a and k such that f is continuous and differentiable for all x.
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(kax if x<2 f(x)=11- kx if 2s x Consider the piecewise function: 6. Find values of the constants a and k such that f is continuous and differentiable for all x.

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Expert Answer

Step 1

The given function is,

Sk + ax
f(x)=11-x
ifx <2
if 2 x
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Sk + ax f(x)=11-x ifx <2 if 2 x

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Step 2

Find the left and right hand limits of the value at the point x = 2.

lim f(x)li(k+ax)
x-2
k4a
lim f(x)lm11 kx)
x2
x--2
11-2k
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lim f(x)li(k+ax) x-2 k4a lim f(x)lm11 kx) x2 x--2 11-2k

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Step 3

Since f(x) is defined and continuous the value of le...

k4a 11-2k
3k 4a 11
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k4a 11-2k 3k 4a 11

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