Various Topics: line eqns, solving log eqns, taking limits,

[dersharpy]

I've been working on my Calc summer assignment(but most material is pre-calc so i figured I should post here). And there's some loose ends I haven't been able to solve. Any help with any problem is appreciated.

1) Write the line equations, y - y₁ = m(x - x₁), for the perpendicular bisector of the line segment with endpoints (3, 2) and (-5, 8)

For this one, I just don't know how to incorporate the perpendicular bisector into what I'm trying to find.

2) Simplify (4/x^3)/(10/x^8)

Should I multiply the the numerator and denominator by x^3 or something like that?

3) Solve the equation: log (x) + log (x + 3) = 1

I am not sure how to solve this. Logs I'm bad with; the process probably involves exponents...?

4) lim_{h -> 0} [(1/(4+h) - (1/4)] / h

I can't figure out how to fix the bottom so that the denominator won't be zero.

I'm sorry if some of those are hard to read. Thanks in advance for any help.

EDIT - Read the rules, made my dilemmas more specific
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Edited by stapel -- Reason for edit: Inserting subjects, verbs, punctuation, etc; unabbreviating words

 

[stapel]

1) Find the slope of the line through the two given points. Review the relationship between the slopes of parallel and perpendicular lines, and find the slope of the perpendicular to this segment. Apply the Midpoint Formula to find the midpoint of the segment. Then, with the slope and the point, plug into the point-slope formula (which you included) to get the required line equation.

2) To multiply fractions, just multiply the numerators by the numerators and the denominators by the denominators. To simplify the exponents, recall what the exponents mean. For instance, x² means (x)(x) and x⁴ means (x)(x)(x)(x), so (x²)(x⁴) means (x)(x)(x)(x)(x)(x) = x²⁺⁴ = x⁶.

3) Use log rules to combine the two logs into one. Then convert the log equation into its equivalent exponential form, and solve the resulting quadratic equation by whatever method you prefer.

...gotta run. Be back with more, if necessary, later.

Eliz.

 

[stapel]

4) A good first step would be to simplify the complex fraction. A common denominator will be useful.

Eliz.

 

[dersharpy]

Thanks for the tips, I'm almost finished with the problems now.