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Are You Ready For Calculus 2?

So, you finished calculus 1. Congratulations! Do you think you are ready for calculus 2? Let's find out. Here are some practice problems from calculus 1 that use techniques that you need for calculus 2. Calculus 2 is the hardest of the three calculus courses and your calculus 1 skills need to be sharp. So here are some problems to help you determine if you are ready.

If you struggle with these problems, don't worry. Use 17calculus to learn what you need to fill in the gaps. Or use these problems to determine where you need to go to refresh your calculus 1 skills, if it's been a while since you took calculus 1.

Here are the main topics you need for calculus 2.

limit techniques

1. basic limits

2. finite limits

3. infinite limits

differentiation techniques

1. basic power and trig rules

2. product rule

3. quotient rule

4. chain rule

applied differentiation

5.maxima and minima

6.equations of tangent lines

integration techniques

1. basic integration

2. integration of basic trig functions

3. integration by substitution

applied integration

4. area between curves

It also helps to go through implicit differentiation and logarithmic differentiation to practice the product rule and the chain rule. The chain rule is the single most important and most used rule of all of the derivative rules. Integration by substitution is the single most important and most used rule of all the integration rules.

Okay, let's get started with some practice problems.

Implicit Differentiation

For explanation of this technique and more practice problems, go to the 17calculus implicit differentiation page.
Instructions - Unless otherwise instructed, calculate \(dy/dx\) by implicit differentiation. Give your answers in simplified, completely factored form.

Question 1

\(x^2+3xy+y^3=10\)

answer

solution

Question 2

\( y^2=(x-y)(x^2+y) \)

answer

solution

Question 3

\(\cos x^2 = xe^y\)

answer

solution

Question 4

\( ye^x+xe^y = xy \)

answer

solution

Question 5

\(\sqrt{xy}=x-4y\)

answer

solution

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