Question

Course Hero Search and extract content from course doc Al Chat with Exit Test Math Knowledg 1. Evaluate: \[ \lim _{x \rightarrow 0} \frac{x^{2}-10 x-25}{x^{2}-5} \] \( -5 \) \( -2 \) 0 2 5 2. If \( g(x)=\lim _{h \rightarrow 0} \frac{\sin (x+h)-\sin x}{h} \), then... \( g(x)=0 \) \( g(x)=1 \) \( g(x)=\cos x \) \( g(x)=\sin x \) 3. If \( y=2 x e^{x} \), find \( y^{\prime \prime} \). (3) \( 19{ }^{\circ} \mathrm{C} \) Sunny

          Course Hero
Search and extract content from course doc
Al Chat with
Exit Test
Math Knowledg
1. Evaluate:
\[
\lim _{x \rightarrow 0} \frac{x^{2}-10 x-25}{x^{2}-5}
\]
\( -5 \)
\( -2 \)
0
2
5
2. If \( g(x)=\lim _{h \rightarrow 0} \frac{\sin (x+h)-\sin x}{h} \), then...
\( g(x)=0 \)
\( g(x)=1 \)
\( g(x)=\cos x \)
\( g(x)=\sin x \)
3. If \( y=2 x e^{x} \), find \( y^{\prime \prime} \).

(3) \( 19{ }^{\circ} \mathrm{C} \)
Sunny

Course Hero
Search and extract content from course doc
Al Chat with
Exit Test
Math Knowledg
1. Evaluate:

limx → 0(x^2-10 x-25)/(x^2-5)

-5
-2
0
2
5
2. If g(x)=limh → 0(sin (x+h)-sin x)/(h), then...
g(x)=0
g(x)=1
g(x)=cos x
g(x)=sin x
3. If y=2 x e^x, find y^''.

(3) 19^∘C
Sunny

Added by Margaret P.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Joseph David

Step 1

- Factor the numerator: \(x^2 - 10x - 25 = (x - 5)(x + 5)\). - The expression becomes \(\frac{(x - 5)(x + 5)}{x^2 - 5}\). - Substitute \(x = 0\) directly: \(\frac{(0 - 5)(0 + 5)}{0^2 - 5} = \frac{-25}{-5} = 5\). Show more…

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Course Hero Search and extract content from course doc Al Chat with Exit Test Math Knowledg 1. Evaluate: \[ \lim _{x \rightarrow 0} \frac{x^{2}-10 x-25}{x^{2}-5} \] \( -5 \) \( -2 \) 0 2 5 2. If \( g(x)=\lim _{h \rightarrow 0} \frac{\sin (x+h)-\sin x}{h} \), then... \( g(x)=0 \) \( g(x)=1 \) \( g(x)=\cos x \) \( g(x)=\sin x \) 3. If \( y=2 x e^{x} \), find \( y^{\prime \prime} \). (3) \( 19{ }^{\circ} \mathrm{C} \) Sunny