Jul 26, 2018 · See graph and details. y = 2 sin pix in 2 [- 1, 1 ] = [ -2, 2 ] Period = ( 2pi )/pi = 2. Amplitude = 2. See graph depicting these aspects.: graph{(y -2 sin (pi x ))(y^2-4)(x^2-1)=0}[-6 6 -3 3] Graph for precisely one half.period, x in [ - 1/2, 1/2 ], using the inverse x-1/pi arcsin(y/2)=0 that does the truncation: graph{x-1/pi arcsin(y/2)=0[-1/2 1/2 -2 2] }

Sep 27, 2015 · d/dx2^(sin(pix))=2^(sin(pix))*ln2*cospix*(pi) Using the following standard rules of differentiation: d/dxa^(u(x))=a^u*lna*(du)/dx d/dx sinu(x) = cosu(x)*(du)/dx d ...

Aug 8, 2016 · 1 lim_{x to 1} sin((pix)/2) =sin((pi)/2) Well, sin((pi)/2) = 1 and the function f(t) = sin t is also continuous in t in (oo, oo)

Oct 29, 2016 · The derivative is dy/dx=pi*ln2*cos(pix)*2^(sin(pix)) Let y=2^(sin(pix)) Taking the logarithms on both sides lny=ln(2^(sin(pix)))=sin(pix)ln2 So taking the derivatives ...

Jan 24, 2017 · If #x in (1, 1/2+sqrt(5)/2)# then #sin(pix) < 0# So in each of the intervals #[1/2 - sqrt(5)/2, 0)# , #(0, 1)# and #(1, 1/2+sqrt(5)/2]# the two functions have opposite signs and cannot intersect. So the only two points of intersection are:

Oct 16, 2015 · Add the form int sin^m u cos^n u du with at least one of m, n odd to your mathematical cookbook. int sin^m u cos^n u du with at least one of m, n odd. Integrate by substitution. Do this by pulling off one from the odd power, then convert the remaining even power to the other function. Integrate the resulting polynomial in sinu or cosu term by term. I = int sin^2pixcos^5 pix dx = int sin ...

Jul 21, 2017 · dy/dx=piln2cos(pix)2^(sinpix) You must write 2^(sinpix) in an other way : y=2^(sinpix)=e^((sinpix)ln2) Now ...

Feb 26, 2017 · Trapezium rule gives: int_2^5 \ sin(pix) \ dx ~~ 0.629062 The values of f(x)=sin(pix) are tabulated as follows (using Excel) working to 5dp Using the trapezoidal rule ...

Mar 6, 2015 · I would use the de l'Hospital Rule. When your limit gives you #0/0# you can derive the numerator and denominator and then do the limit.

Sep 23, 2016 · How do you find the intersections points of #y=2cos(2pix)# and #y=-2sin(pix)#? Trigonometry Graphing Trigonometric Functions General Sinusoidal Graphs 1 Answer