I don't know how do this, I know that I use L'hopitals Rule, I just don't know who to start.

1 answer:

5 0

Lim[x.sin(4π/x)] when x →∞. To apply the Hospital rule we need a fraction:

lim[x.sin(4π/x)] could be written:

lim [sin(4π/x)] / (1/x) . Now let's find the derivative of the numerator and the denominator:

Numerator = sin(4π/x) → (Numerator)' = cos(4π/x).(-4π/x²) [Chaine rule
(sinu)' = cosu. u'] So derivative of Numerator = cos(4π/x).(-4π/x²)

Denominator = 1/x → Numerator derivative = -1/x²

Now : (numerator)'/(denominator)' = cos(4π/x).(-4π/x²) / -1/x²
Simplify by x² : → cos(4π/x).(-4π) / -1

OR cos(4π/x).(4π) . When x→∞ , 4π/x → 0 and cos(0) = 1, then:

lim[x.sin(4π/x)] when x →∞. is 4π

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I need help finding the area

aniked [119]

<h3>Given :</h3>

Base of triangle = 7 yd
Height of triangle = 10 yd

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Area of triangle

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We know:-

When base and height of triangle is given we use this formula:

$\bigstar \boxed{ \rm Area \: of \: triangle = \frac{base \times height}{2} }$

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So:-

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$\dashrightarrow \sf \: Area \: of \: triangle = \dfrac{base \times height}{2} \\$

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$\dashrightarrow \sf \: Area \: of \: triangle = \dfrac{7 \times 10}{2} \\$

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$\dashrightarrow \sf \: Area \: of \: triangle = \dfrac{7 \times 5 \times2 }{2} \\$

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$\dashrightarrow \sf \: Area \: of \: triangle = \dfrac{7 \times 5 \times\cancel2 }{\cancel2} \\$

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$\dashrightarrow \sf \: Area \: of \: triangle = \dfrac{7 \times 5 \times1 }{1} \\$

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$\dashrightarrow \sf \: Area \: of \: triangle =7 \times 5$

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$\dashrightarrow \bf \: Area \: of \: triangle =35 {yd}^{2} \\$

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$\therefore \underline{\textsf{ \textbf {\: Area \: of \: triangle = \red{35}}} { \red{\bf{yd} }^{ \red2} }}$

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$\small\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin {array}{cc}\\ \dag\quad \Large\underline{\bf \small{Formulas\:of\:Areas:-}}\\ \\ \star\sf Square=(side)^2\\ \\ \star\sf Rectangle=Length\times Breadth \\\\ \star\sf Triangle=\dfrac{1}{2}\times Base\times Height \\\\ \star \sf Scalene\triangle=\sqrt {s (s-a)(s-b)(s-c)}\\ \\ \star \sf Rhombus =\dfrac {1}{2}\times d_1\times d_2 \\\\ \star\sf Rhombus =\:\dfrac {1}{2}d\sqrt {4a^2-d^2}\\ \\ \star\sf Parallelogram =Base\times Height\\\\ \star\sf Trapezium =\dfrac {1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac {\sqrt{3}}{4}(side)^2\end {array}}\end{gathered}\end{gathered}\end{gathered}$ ]