# Calculus

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Find the value of c where the line l tangent to the graph of y=2.5*5^x at (0,2.5) intersects the x-axis

• Calculus -

dy/dx = 2.5(5^x)ln5
when x=0 from (0, 2.5)
dy/dx = 2.5ln5

so tangent is y= 2.5ln5 x + c
at (0 , 2.5)
2.5 = 0 + c
so the equation is y = 2.5ln5 x + 2.5
at the x-axis, y =0
0 = 2.5ln5 x + 2.5
2.5ln5 x = -2.5
ln5 x = -1
x = -1/ln5 or appr -.62

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