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You have to be able to remember the conditions for perpendicular lines . Hint try finding out how their slopes are related and you are on the right track

remember the formula for finding slope
Y2-Y1/X2-X1=m
so we are giving Y2=2a,Y1=a,X2=5,X1=3 and m=1/3
2a-a/5-3=1/3
a/2=1/3
by cross multiplying we have 3a=2
a=2/3

I have 3 very tricky limits questions


1 lim (x sin(x^2 e^x))/(x^2 1) as x approaches infinity.

2 lim(1/(e^x sin(1/x^2)) as x approaches infinity

3 lim(x-x^1/2 lnx) as x approaches...

Thank you so much u explained clearly

let f and g be differentiable functions on (-infinity;infinity) such that f′(a) > 0 for all a and g′(b) < 0
for all b > 0. Let h(x) = f(g(x^2)). Find the open intervals on which h is increasing...