Each of these limits correspond to the derivative of some function <em>f(x)</em> at a point <em>x</em> = <em>a</em>.
Recall the limit definition of a function <em>f(x)</em> :
<em>f '(x)</em> = lim [<em>h</em> → 0] ( <em>f(x</em> + <em>h)</em> - <em>f(x) </em>) / <em>h</em>
Then if <em>x</em> = <em>a</em>, we get
<em>f '(a)</em> = lim [<em>h</em> → 0] ( <em>f(a</em> + <em>h)</em> - <em>f(a) </em>) / <em>h</em>
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From here, it's easy to identify what each function and point should be:
(a) <em>f </em>(<em>a</em> + <em>h</em>) = (1 + <em>h</em>)¹ʹ³ → <em>f(x)</em> = <em>x </em>¹ʹ³ and <em>a</em> = 1
(that's a 1/3 in the exponent)
(b) <em>f</em> (<em>a</em> + <em>h</em>) = cos(<em>π</em> + <em>h</em>) → <em>f(x)</em> = cos(<em>x</em>) and <em>a</em> = <em>π</em>
<em />
(c) <em>f</em> (<em>a</em> + <em>h</em>) = 5 (4 + <em>h</em>)⁵ → <em>f(x)</em> = 5<em>x</em> ⁵ and <em>a</em> = 4
(d) <em>f</em> (<em>a</em> + <em>h</em>) = exp(4<em>h</em>) = exp(4 (0 + <em>h</em>)) → <em>f(x)</em> = exp(4<em>x</em>) and <em>a</em> = 0
(where exp(<em>x</em>) = <em>eˣ </em>)
The answer is A, since the width of the new office was going to be 15 feet longer
5×395=5×(400-5)
Hope this helps!
$11.25/ 1.55 pounds= $7.26/pound.
The unit rate for a piece of cheese is $7.26/pound~
Answer:
-1
Step-by-step explanation:
Start with F(x - 1) = 2x + 3. Rewrite the right side (2x + 3) as follows:
F(x - 1) = 2[ x ] + 3
F(x - 1) = 2[ x - 1 + 1 ] + 3 = 2 [ (x - 1) + 1 ] + 3
= 2 (x - 1) + 2 + 3
= 2(x - 1) + 5
To evaluate F(-3), replace "x - 1" with "-3" :
F(-3) = 2(-3) + 5 = -1
