What is the limit as x approaches infinity of ex?
When x takes the value infinity, it becomes. e∞ = ∞ \(\begin{array}{l}\lim_{x\rightarrow \infty }e^{x}\end{array} \)=∞
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Verify that cos 2x = 2 cos2 x -1
\(\begin{array}{l}\cos 2x =\cos ^{2}x -\sin ^{2}x\end{array} \)——(i) We have learnt that \(\begin{array}{l}\cos ^{2}x + \sin ^{2}x=1\end{array} \) So \(\begin{array}{l}\sin ^{2}x=1... View Article
Solve cos 2θ + sin θ + 1 = 0
cos2θ + sin θ + 1 = 0 ⇒ (1 – sin2θ) + sin θ + 1 = 0 ⇒... View Article
The derivative of cos 3x w.r.t. sin 3is
Let u = cos3x and v = sin3x On differentiating we get \(\begin{array}{l}\frac{du}{dx}=-3\cos ^{2}x sin x\end{array} \) =\(\begin{array}{l}\frac{dv}{dx}=3\sin ^{2}x \cos... View Article
What is the tangent ratio at 15 degrees?
Tan (15°) = sin 15/cos 15 Tan 15° = sin 15/cos 15 Sin 15° = sin (45 – 30)° and... View Article
Simplify (sec2x) – (tan2x) using sin and cos
We know the identity sin2(x)+cos2(x)=1 ——-(i) Dividing throughout the equation by cos2(x) We get sin2(x)/cos2(x) + cos2(x)/cos2(x) = 1/cos2(x) We... View Article
sec 2x – tan 2x in terms of tan is _________?
sec 2x – tan 2x (1/cos 2x) – (sin 2x/cos 2x) = (1 – sin 2x)/cos 2x Using the identities,... View Article
What is the derivative of f(x) = cos-1(x) ?
Solution Let us assume y= cos-1x By Differentiate Implicitly -sin y dy/dx= -1————-(i) By trigonometric identity we know that \(\begin{array}{l}sin... View Article
Prove that 12 + 22 + 32 + … + n2 = 1/6n(n + 1)(2n + 1)?
Let p(n)=12+22+32+….+n2= n(n+1)(2n+1)/ 6 For n = 1, the statement reduces to 12 =1 · 2 · 3/6 and is... View Article
How do you simplify the expression 1-sec2x?
We know the identity \(\begin{array}{l}\sec ^{2}x +\tan ^{2}x =1\end{array} \) On simplyfing the identity we get \(\begin{array}{l}1 -\sec ^{2}x =... View Article
What is the integral of int tan4x dx?
\(\begin{array}{l}\int \tan ^{4}x dx\end{array} \) Solution \(\begin{array}{l}\int \tan ^{4}x dx\end{array} \) can be written as = \(\begin{array}{l}\int \tan ^{4}x -1... View Article
Integrate cot x cos x dx
\(\begin{array}{l}\int \cot x \cos x dx\end{array} \) Solution Will express cot x in terms of sin and cos. Hence the... View Article
How do you find lim cosx/x as x->0?
\(\begin{array}{l}\lim_{x\rightarrow 0}\frac{cos x}{x}=\infty\end{array} \) Explanation \(\begin{array}{l}\lim_{x\rightarrow 0}\frac{cos x}{x}\end{array} \) As \(\begin{array}{l}x\rightarrow 0\end{array} \) \(\begin{array}{l}cosx\rightarrow cos 0 = 1\end{array} \) and... View Article
How do I find 2/3 of a whole number?
The whole numbers are the numbers without fractions and it is a collection of positive integers and zero. It is... View Article
Explain tan 2x formula
\(\begin{array}{l}Tan 2x =\frac{2tan x}{1-tan^{2}x} \end{array} \) Derivation Tan 2x =\frac{2tan x}{1-tan^{2}x} \end{array} \) As per the addition formula. \(\begin{array}{l}tan(a+b) =\frac{... View Article
What’s the LCM of 4, 5 and 10?
The LCM is the smallest positive number that all the numbers divide into evenly. Write out the multiples of 4,5... View Article
What are the prime factors of 57?
As the sum of the digits of 57 is 12, a multiple of 3, hence, 57 is divisible by 3.... View Article
The atomic mass of silver found in nature is Ar (Ag) = 107,983. This silver is made of 107Ag and 109Ag Isotopes. Calculate the proportion of mass of 107Ag isotope which is in natural silver atoms?
If x is the fraction of Ag107 and y is the fraction of Ag109 then we can write: (107×x) +... View Article
What is scattering angle?
The angle between the initial and final directions of motion of a scattered particle is called scattering angle. Also known... View Article
Why is DNA called the blueprint of life?
Structure of DNA was established by James Watson and Francis Crick. The shape of DNA is a double helix.DNA is... View Article
