Answer:
<h2><em><u>18</u></em></h2>
Step-by-step explanation:
<em><u>Given</u></em><em><u>, </u></em>
Radius of the cylinder = 3cm
Height of the cylinder = 3cm
<em><u>Therefore</u></em><em><u>, </u></em>
Lateral surface area of the cylinder




<em><u>Hence</u></em><em><u>,</u></em>
<em><u>The</u></em><em><u> </u></em><em><u>required</u></em><em><u> </u></em><em><u>value</u></em><em><u> </u></em><em><u>in</u></em><em><u> </u></em><em><u>the</u></em><em><u> </u></em><em><u>green</u></em><em><u> </u></em><em><u>box</u></em><em><u> </u></em><em><u>will</u></em><em><u> </u></em><em><u>be</u></em><em><u> </u></em><em><u>18</u></em><em><u> </u></em><em><u>(</u></em><em><u>Ans</u></em><em><u>)</u></em>
Step-by-step explanation:
Height of ladder = 12ft .
Here perpendicular is height to which it reaches .
<u>When </u><u>angle </u><u>is </u><u>3</u><u>0</u><u>⁰</u><u> </u><u>:</u><u>-</u>
=> sin 30⁰ = H/12
=> ½ = H/12
=> H = 12/2
=> H = 6m ( ans )
<u>When </u><u>Angle </u><u>is </u><u>4</u><u>5</u><u>⁰</u><u> </u><u>:</u><u>-</u><u> </u>
=> sin45⁰ = H/12
=> 1/√2 = H/12
=> H = 6*√2*√2/√2
=> H = 6√2 m ( ans )
<u>When </u><u>angle</u><u> </u><u>is </u><u>6</u><u>0</u><u>⁰</u><u> </u><u>:</u><u>-</u>
=> sin60⁰ = H/12
=> √3/2 = H/12
=> H = 12 *√3/2
=> H = 6√3 ( ans )
hope it helped !
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#2) Use quotient rule

Remember for solving log equations:

#3) Derivative of tan = sec^2 = 1/cos^2
Domain of tan is [-pi/2, pi/2], only consider x values in that domain.
#4 Use Quotient rule
#9 Use double angle identity for tan

This way you can rewrite tan(pi/2) in terms of tan(pi/4).
Next use L'hopitals rule, which says the limit of indeterminate form(0/0) equals limit of quotient of derivatives of top/bottom of fraction.
Take derivative of both top part and bottom part separately, then reevaluate the limit. <span />