Answer:
108
Step-by-step explanation:
Limit as x approaches 9 of x^2 -81/sqrt of x - 3
First substitute x into the expression
= 9²-81/√9 - 3
= 81-81/3-3
= 0/0 (indeterminate)
Apply l'hospital rule
= lim x -> 9 d/dx(x²-81)/√x - 3
= lim x -> 9 2x/1/2√x
Substitute x = 9
= 2(9)/1/2√9
=18/1/(2(3)
=18 × 6/1
= 108
Hence the limit of the function is 108
Value of y= 18 and value of x= 9 root3
therefore answer is D
Answer:
in steps
Step-by-step explanation:
upper square: P = 20x² + 8
<u>side: P/4 = 5x² + 2</u>
<u>A = side² = (5x² + 2)² = 25x⁴ + 20x² + 4</u>
Middle equilateral Triangle: A = x² + 4x + 4 base = 2x + 4
A = base x height / 2
(x + 2)² = 2 (x + 2) x height /2
<u>height = x + 2</u>
<u>perimeter = 2 (x + 2) x 3 = 6x + 12</u>
Lower trapezoid: A₁ = 2x² + 24x + 40 = 2 (x² + 12x + 20) = 2 (x + 2) (x + 10)
A₁ = (x + 10)² = 2 (x + 2) (x + 10)
x + 10 = 2x + 4
x = 6
<u>A₂ = (2x + 4) (x + 10) / 2 = (16 x 16) / 2 = 128</u>
A₁ = (6 + 10)² = 256
<u>AT = 256 + 128 = 384</u>
Answer:
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