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15. Simplify sin(90° - O) cos 0 - sin(180° +0) sin e.​

Answers

Answer 1
Answer:

Answer:  cos²(θ) + sin(θ)sin(e)

Step-by-step explanation:

sin (90° - θ)cos(Ф) - sin(180° + θ) sin(e)

Note the following identities:

sin (90° - θ) = cos(x)

sin (180° + θ) = -sin(x)

Substitute those identities into the expression:

   cos(x)cos(x)  -  -sin(x)sin(e)

=  cos²(x) + sin(x)sin(e)

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Find the limit of the formula given​

Answers

Answer:

\displaystyle \lim_(x \to 0^+) x^\big{√(x)} = 1

General Formulas and Concepts:

Algebra II

  • Natural logarithms ln and Euler's number e
  • Logarithmic Property [Exponential]:                                                             \displaystyle log(a^b) = b \cdot log(a)

Calculus

Limits

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

Limit Rule [Variable Direct Substitution]:                                                             \displaystyle \lim_(x \to c) x = c

L’Hopital’s Rule:                                                                                                     \displaystyle \lim_(x \to c) (f(x))/(g(x)) = \lim_(x \to c) (f'(x))/(g'(x))

Differentiation

  • Derivatives
  • Derivative Notation

Basic Power Rule:

  1. f(x) = cxⁿ
  2. f’(x) = c·nxⁿ⁻¹  

Step-by-step explanation:

We are given the following limit:

\displaystyle \lim_(x \to 0^+) x^\big{√(x)}

Substituting in x = 0 using the limit rule, we have an indeterminate form:

\displaystyle \lim_(x \to 0^+) x^\big{√(x)} = 0^0

We need to rewrite this indeterminate form to another form to use L'Hopital's Rule. Let's set our limit as a function:

\displaystyle y = \lim_(x \to 0^+) x^\big{√(x)}

Take the ln of both sides:

\displaystyle lny = ln \Big( \lim_(x \to 0^+) x^\big{√(x)} \Big)

Rewrite the limit by including the ln in the inside:

\displaystyle lny = \lim_(x \to 0^+) ln \big( x^\big{√(x)} \big)

Rewrite the limit once more using logarithmic properties:

\displaystyle lny = \lim_(x \to 0^+) √(x)ln(x)

Rewrite the limit again:

\displaystyle lny = \lim_(x \to 0^+) (ln(x))/((1)/(√(x)))

Substitute in x = 0 again using the limit rule, we have an indeterminate form in which we can use L'Hopital's Rule:

\displaystyle \lim_(x \to 0^+) (ln(x))/((1)/(√(x))) = (\infty)/(\infty)

Apply L'Hopital's Rule:

\displaystyle \lim_(x \to 0^+) (ln(x))/((1)/(√(x))) = \lim_(x \to 0^+) \frac{(1)/(x)}{\frac{-1}{2x^\big{(3)/(2)}}}

Simplify:

\displaystyle \lim_(x \to 0^+) \frac{(1)/(x)}{\frac{-1}{2x^\big{(3)/(2)}}} = \lim_(x \to 0^+) -2√(x)

Redefine the limit:

\displaystyle lny = \lim_(x \to 0^+) -2√(x)

Substitute in x = 0 once more using the limit rule:

\displaystyle \lim_(x \to 0^+) -2√(x) = -2√(0)

Evaluating it, we have:

\displaystyle \lim_(x \to 0^+) -2√(x) = 0

Substitute in the limit value:

\displaystyle lny = 0

e both sides:

\displaystyle e^\big{lny} = e^\big{0}

Simplify:

\displaystyle y = 1

And we have our final answer.

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

Unit:  Limits

Please hurry need help

Answers

Answer:

-11

Step-by-step explanation:

Please help me solve this math problem

Answers

Answer:

I think it is undefined.

Insert <, >, or = between the given pair of numbers to make a true statement.- |-11| - (-11)

Answers

Answer:

- |-11| < - (-11)

Step-by-step explanation:

Given the pair of numbers - |-11| and - (-11), we want to determine which is greater or whether they are equal

First lets rewrite both numbers.

- |-11| = -11 (note that the modulus sign will change any negative value into a positive value and that's why |-11| is equivalent to 11)

- (-11)  = 11 (note that the negative sign here was retained since it is not an absolute value like the former)

It can be seen that both numbers are therefore not equal i.e  - |-11| is less than  - (-11). Hence the expression - |-11| < - (-11) is a true statement

How many cups are in 3 gallons? 1 gallon = 16 cups
Label your answer in cups.

Answers

Answer:

There are 48 cups in 3 gallons!

Hope this helped! :)

This graph shows a proportional relationship.What is the constant of proportionality?
Enter your answer in the box.

Answers

Hey, this is worked out the same way as the last problem you posted!

Remember that constant of proportionality is slope...

(y2-y1) ÷ (x2 -x1)

↓

(225 - 135) ÷ (5 - 3)

↓

90 ÷ 2

↓

45

The constant of proportionality is 45

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