Basic Calculus :)

It is the process of finding the antiderivative of a function and the opposite process of differentiation.

• limit of a function

• differentiation

• antidifferentiation

• derivative of a function

Which of the following is the antiderivative of  $\int x^{\frac{1}{2}}dx$  ?

•  $x^{\frac{1}{2}}+C$  

•  $x+C$  

•  $\frac{2x^{\frac{3}{2}}}{3}+C$  

•  $2x+C$  

The derivative of  $f\left(x\right)=x^5$  is  $f'\left(x\right)=5x^4$  .

• FACT

• BLUFF

The derivative of  $f\left(x\right)=x^5$  is  $f'\left(x\right)=5x^4$  .

• FACT

• BLUFF

What is the antiderivative of  $\int3dx$  ?

(a)  

Evaluate  $\int\left(10x^4-4x^3+6x^2-2\right)dx$ .

•  $40x^3-12x^4+12x^3$  

• does not exist

•  $2x^5-x^4+2x^3-2x+C$  

•  $2x^5-x^4+2x^3-C$  

It occurs when the instantaneous rate of change of a quantity with respect to time is proportional to the quantity itself

• Exponential growth

• The law of logarithm

• Decaying process

• the process of differentiation

In bounded growth and logistic growth, L is the carrying capacity of the population.

• The statement is true.

• The statement is false.

• The statement has no sense.

• The statement is confusing.

The population of a certain kind of fleas grows exponentially. If the initial population of fleas was 1, 500 after 5 days the population was 9, 000. Find the growth rate of the population of fleas.

• 3.33

• 0.48

• 0.24

• 0.133

Tags

CCSS.HSF.LE.A.4

This theorem states that if we can find an antiderivative for the integrand, then we can evaluate the definite integral by evaluating the antiderivative at the endpoints of the interval and subtracting

• Theorem of Differentiation

• Antiderivative Theorem

• Fundamental Theorem of Calculus