Another week down and first nine weeks exams are creeping up on us. This means it is study guide time.
In the study guide there are limits. The limit rules are: 1) if the highest exponent is the same on the top and bottom then the limit is the top coefficient over the bottom coefficient of the highest exponents. 2) If the highest exponent is on the top then the limit is infinity. 3) But if the highest exponent is on the bottom then the limit is 0.
Some examples are:
lim->infinity (3x^2-2x)/(2x^2+4x-1) Then the limit is 3/2 because it follows rule 1.
lim->infinity (8x^4+6)/(3x-9) Then the limit is infinity because it follows rule 2.
lim->infinity (x-7)/(5x^3+4x+2) Then the limit is 0 because it follows rule 3.
Also the study guide reviews taking derivivatives. That means using the product rule, quotient rule, and the regular way of taking the derivative of an equation.
Product rule is copy the first times the derivative of the last plus copy the first times the derivative of the second.
Quotient rule is copy the bottom times derivative of the top minus copy the top times the derivative of the bottom all divided by the bottom squared.
But there are some things I do not remember how to do or never did. I do not remember how to do the tangent line things. And I still do not fully understand optimization. Help with these 2 things would be great so that I will be ready for the exam.
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Okay, so a tangent line touches a graph at only one point.
ReplyDeleteall you do is take the derivative of the first equation to get the slope, then using the graph of the other line given to you, find a point on the graph that they share and plug it in to find the y-value. then use the point slope formula
To find the equation of a tangent line, you first have to find your y value if it is not given and you do this by plugging your given x value into the equation. Then you have to take the derivative of the equation and plug in x to find your slope. The next step is to put it into point slope form which is y-y1=m(x-x1). You leave it in this form unless your multiple choice answers are in standard form.
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