LHL in not equal to RHL , Therefore the limit does not exists , Option D is the answer.(none)
<h3>What is the limit of a function ?</h3>
The limit of a function at a certain point is the value that the function approaches as the argument of the function approaches the same point.
It is given that
lim x->2 for f(x)
f(x) = 2x+1 x ≤2
f(x)= x² , x >2
When both the function tends to 2
Left Hand Limit
f(x) = 2 *2 +1
f(x) = 5
Right Hand Limit
f(x) = x² ,
f(x) = 4
LHL in not equal to RHL , Therefore the limit does not exists.
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Answer:
A
Step-by-step explanation:
the maximum turning point is on the top and minimum on the bottom in this case maximum Is above the X-axis
Answer:
12
Step-by-step explanation:
f(x)=x^+4x+2 First, let's evaluate when x=3, x=4 and x=5.
f(3) = 3²+4(3)+2 = 9 + 12 + 2 = 23
f(4) = 4²+4(4)+2 = 16 + 16 + 2 = 34
f(5) = 5²+4(5)+2 = 25 + 20 + 2 = 47
Now, let's find the rate of change.
34 - 23 = 11
47 - 34 = 13
Finally, the average rate of change.
(11 + 13) / 2 = 12
This problem requires the use of the chain rule: dy / dt = [dy / dx] * [dx / dt]
y = √x => dy / dx = 1 / (2√x)
<span>(a) Find dy/dt, given x = 16 and dx/dt = 7.
dy/dt = [ 1/(2√x) ] * 7 = [1/(2*4)] * 7 = 7/8
(b) Find dx/dt, given x = 64 and dy/dt = 8.
dx/dt = [dy/dt] / [dy/dx] = 8 / [1/(2√64) ] = 128
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