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Lauren L.
Tutor for 6 years
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Calculus
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Question:

Find the limit as x approaches infinity of x/(1+3x)

Lauren L.

If we let x tend to infinity in this expression we get infinity/infinity, which in indeterminate. So, we need to manipulate the expression in such a way that we get a solution that is not indeterminate. Now, having terms with x in both the numerator and denominator is what is causing problems, so if we can factor an x from the denominator, we can cancel it with the x in the numerator. First we factor x in the denominator: x/(x((1/x)+3)) Now we can cancel the x in the numerator and the denominator to get: 1/((1/x)+3) Now if we let x tend to infinity 1/x goes to 0, so we are left with 1/(0+3)=1/3 so our limit as x tends to infinity is 1/3

Algebra
TutorMe
Question:

Simplify: (4-16i)+(-1+7i)

Lauren L.

When adding and subtracting complex numbers we treat i as if it is a variable, meaning we can only combine terms that have i with other terms that have i (like terms). First we can rewrite the expression without the brackets 4-16i-1+7i First we can combine the constant terms by adding 4+(-1)=3, leaving us with: 3-16i+7i Now we combine the terms with i by adding -16i+7i=-9i, leaving us with 3-9i Which is our solution

Algebra
TutorMe
Question:

Solve for x: -2x+10=4

Lauren L.

-2x+10=4 The goal here is to isolate our variable, x. Since we are dealing with an equation, we can preform the same operation to both sides so that they remain equal. Now, the left side of the equation contains two terms, one with x and one without. So, first we want to isolate the term that has x. We do this by subtracting 10 from both sides of the equation. -2x+10-10=4-10 -2x=-6 Now on the left hand side we have -2x. Here, x is being multiplied by -2, so to isolate x we want to divide by -2, so that our coefficient of x becomes one. (-2/-2)x=-6/-2 x=3 Now we have our answer x=3

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