hadejada7x
2022-01-16
Answered

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Vivian Soares

Answered 2022-01-17
Author has **36** answers

If you can use Taylor series, the numerator is

$x(1+a-\frac{a{x}^{2}}{2})-b(x-\frac{{x}^{3}}{6})+o\left({x}^{3}\right)=(1+a-b)x+(b-3a)\frac{{x}^{3}}{6}+o\left({x}^{3}\right)$

Solving$1+a-b=0,b-3a=6$ gives $a=-\frac{52}{,}b=-\frac{32}{}$

Solving

kaluitagf

Answered 2022-01-18
Author has **38** answers

Apply LHopitals rule again:

$\underset{x\to 0}{lim}\frac{x(1+a\mathrm{cos}x)-b\mathrm{sin}x}{{x}^{3}}\stackrel{LHR}{=}\underset{x\to 0}{lim}\frac{1+(a-b)\mathrm{cos}x-ax\mathrm{sin}x}{3{x}^{2}}$

$\stackrel{LHR}{=}\underset{x\to 0}{lim}\frac{(b-2a)\mathrm{sin}x-ax\mathrm{cos}x}{6x}$

and recall that$\underset{x\to 0}{lim}\frac{\mathrm{sin}x}{x}=1$

and recall that

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Airline passengers arrive randomly and independently at the passenger-screening facility at a major international airport. The mean arrival rate is 11 passengers per minute.

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Proving $\frac{\mathrm{csc}x+\mathrm{cot}x}{\mathrm{tan}x+\mathrm{sin}x}=\mathrm{cot}x\mathrm{csc}x$

asked 2021-12-31

The Question

$\int \mathrm{csc}(x-\frac{\pi}{3})\mathrm{csc}(x-\frac{\pi}{6})dx$

What I Tried- I tried dividing both numerator and denominator by$\mathrm{sin}\frac{\pi}{6}$ but couldnt

What I Tried- I tried dividing both numerator and denominator by

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Use a calculator to find the solution of teh equation, rounded to six decimal places.

$5}^{2x+1}={3}^{4x-1$

asked 2022-01-02

How do I evaluate $\underset{z\to 1}{lim}(1-z)\mathrm{tan}\frac{\pi z}{2}$

I tried using the identity,$\mathrm{tan}\frac{x}{2}=\frac{1-\mathrm{cos}x}{\mathrm{sin}x}$ to simplify this to:

$\underset{z\to 1}{lim}(1-z)\frac{\mathrm{sin}\pi z}{1+\mathrm{cos}\pi z}$

I tried using the identity,

asked 2021-12-31

If $\frac{1-\mathrm{sin}x}{1+\mathrm{sin}x}=4$ , what is the value of $\mathrm{tan}\frac{x}{2}$ ?

1)-3

2)2

3)-2

4)3

1)-3

2)2

3)-2

4)3