MATHEMATICS HIGH SCHOOL

Use graphs and tables to find the limit and identify any vertical asymptotes of limit of 1 divided by the quantity x minus 3 as x approaches 3 from the left.

Answers

Answer 1

Answer:

Answer:

$\displaystyle \lim_( \to 3^-) (1)/(x - 3) = -\infty$

General Formulas and Concepts:

Calculus

Limits

Right-Side Limit: $\displaystyle \lim_(x \to c^+) f(x)$
Left-Side Limit: $\displaystyle \lim_(x \to c^-) f(x)$

Graphical Limits

Step-by-step explanation:

If we graph the function, we can see that as we approach 3 from the left, we go towards negative infinity.

∴ $\displaystyle \lim_( \to 3^-) (1)/(x - 3) = -\infty$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Limits

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A triangular region of the community college parking lot was measured. The measure of the first angle of this triangle is double the measure of the second angle. The measure of the third angle is 19° greater than double the measure of the first angle. What are the measurements of all three angles?

Answers

The key to word problems like this is to turn them into an equation, then they are much simpler to solve.
The first angle is is double the second, so it will be 2x and the second angle will be x. The third angle is 19 more than double the measure of the first angle. that means its 4x +19.

Hope ypu understand it

21. find the volume of the solid of revolution formed if the area enclosed between the curves y=x² and y=(x-2)² is rotated about the x-axis using integration

Answers

What you need to do is get hold of the area underneath the curve y=x² from x=1 to x=0. You then spin this area 360 degrees about the x-axis and double the result as there is symmetry between y=x² and y=(x-2)².

Use the formula:

$Volume=\int _( a )^( b ){ \pi { y }^( 2 ) } dx$

Ok, so let's solve the problem...

$V=2\int _( 0 )^( 1 ){ \pi { x }^( 4 ) } dx\n \n =2{ \left[ \frac { \pi { x }^( 4+1 ) }{ 4+1 } \right] }_( 0 )^( 1 )$

$\n \n =2{ \left[ \frac { \pi { x }^( 5 ) }{ 5 } \right] }_( 0 )^( 1 )\n \n =2\left\{ \left( \frac { \pi }{ 5 } \right) -\left( 0 \right) \right\} \n \n =\frac { 2 }{ 5 } \pi$

Answer:

$\frac { 2 }{ 5 } \pi$ units cubed.

Two similar pyramids have corresponding dimensions in the ratio 3:5 Find the ratio of their volumes