Answers created by Bill K.

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• For which natural numbers "n" is irrelevance?
  
• If `f(x)=lim_(n->oo)1/(1+nsin^2pix)` , find the value of `f(x)` for all real values of `x`?
  
• How do you find the partial sum of `Sigma (250-8/3i)` from i=1 to 60?
  
• Evaluate the integral or show that it is divergent?
  
• How do you use implicit differentiation to find the slope of the curve given `xy^2+x^2y=2` at (1,-2)?
  
• Show the first three terms in the expansion of `1/(1-(x/2))^3` in ascending powers of x?
  
• How do you prove by definition that the function `f(x)= x^2 sin (1/x)` is continuous at x=0?
  
• How do you apply the ratio test to determine if `sum_(n=2)^oo 10^n/(lnn)^n` is convergent to divergent?
  
• Be f : A → B a function and X,Y ⊂ B. Show that: any thoughts? thanks
  
• Prove the absolute convergence of the series?
  
• Find all zeros: `f(x)=3x^7-32x^6+28x^5+591x^4-1181x^3-2810x^2+5550x-1125`?
  
• May I know how to solve it?? Thank you
  
• Question #f58b3
  
• How do you find the sum of the infinite geometric series `Sigma -10(0.2)^n` from n=0 to `oo`?
  
• Question #daa0e
  
• Question #7a02c
  
• Question #2538f
  
• Question #e4f55
  
• How do you test the improper integral `int x/absxdx` from `[-5,3]` and evaluate if possible?
  
• Question #c64ae
  
• Question #0c7d0
  
• How to choose the Bn for limit comparison test?
  
• Question #0ffa1
  
• Given two functions `f` and `g`, what is the inverse of `g @ f` ?
  
• How do you use Taylor series to estimate the accuracy of approximation for `f(x)=sqrt(x)` with `a=1` and `n=3` with `0.9<=x<=1.1`?
  
• Question #143f6
  
• Question #2880c
  
• Question #373e2
  
• Question #2849d
  
• Question #9f75a
  
• If students toss a coin 200 times each, about 68% should have proportions between what two numbers?
  
• How do you simplify `\frac { 4t - 16} { t ^ { 2} - 16}`?
  
• Question #19089
  
• Question #2e37e
  
• How do you differentiate `y=sin(xy)`?
  
• Question #cafe0
  
• Given the function `f(x)=((x)/(x+4))`, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [1,8]?
  
• Let V=`RR^3` and W={(x,y,z)|x,y,z `in` `QQ`}. Is W`<=`V? Justify your answer.
  
• How do you integrate `inte^(x^2)sin^2xdx` using integration by parts?
  
• Question #041ca
  
• How do you use the Fundamental Theorem of Calculus to find the derivative of `int (cos(t^4) + t) dt` from -4 to sinx?
  
• Why is `y=1/x` a continuous function?
  
• Find a number such that for all x, 0 < < δ ⇒ < ε.???? f(x) = 6x - 9, L = -3, x0 = 1, and ε = 0.01 0.001667 0.01 0.003333 0.000833
  
• True or false? A series `oo` `sum_(n=1)alpha_n` is convergent if `lim_(n->oo)S_n` converges. ( `S_n` = nth partial sum)
  
• For a standard normal distribution, how do you find the percentage of data that are between 3 standard deviations below the mean and 1 standard deviation above the mean?
  
• How to evaluete: `int_0^(pi/2) e^(sinx)*cosxdx` ?
  
• Question #b2c2c
  
• How do you solve `\frac { v + 1} { v } = \frac { 8} { 10}`?
  
• Is the gender of the next baby born at a particular hospital categorical or numerical? How can you tell?
  
• How do you find the slope of the regression line for the following set of data?
  
• How does central tendency relate to normal distribution?
  
• Question #47ab6
  
• Question #aa562
  
• Question #41397
  
• Question #f06e5
  
• How can type 1 and type 2 errors be minimized?
  
• Question #c27db
  
• Question #4bd79
  
• Question #9eb92
  
• How do you find the distance travelled from t=0 to `t=2pi` by an object whose motion is `x=cos^2t, y=sin^2t`?
  
• What are continued fractions for?
  
• How do you integrate `int e^(5x)cos3x`?
  
• Question #e382d
  
• Find the volume of the solid of revolution obtained by rotating the curve `x=3cos^3theta` , `y=3sin^3theta` about the `x` axis?
  
• How do you divide `( 3i-7) / ( 2 i -1 )` in trigonometric form?
  
• How do you differentiate `y=ln[(x+9)^6(x+6)^2(x+5)^3]`?
  
• How do you write the equation `y=(x-2)^2+ 6` in standard form?
  
• Question #14068
  
• How do you find the critical numbers of `f(x)=x^(2/3)+x^(-1/3)`?
  
• How do you use the binomial series to expand `x^4/(1-3x)^3`?
  
• How do you solve `|x ^ { 2} - 32| > 4`?
  
• `\int_t^5(dt)/((t-4)^2)`?
  
• Are the power, type 1, and type 2 error values p-values?
  
• A normally distributed data set has a mean of 53 and a standard deviation of 2.5. What Z-score corresponds to a data value of 47?
  
• Question #3f147
  
• How do you find the average value of the function for `f(x)=sqrtx+1/sqrtx, 1<=x<=9`?
  
• How do you find the distance travelled from t=0 to t=1 by a particle whose motion is given by `x=4(1-t)^(3/2), y=2t^(3/2)`?
  
• Question #68d98
  
• Question #ef682
  
• How do you solve `|5v + 3| > - 9`?
  
• Suppose `T_4(x) = 7-3(x-2)+7(x-2)^2-6(x-2)^2+8(x-2)^4` is the degree 4 Taylor polynomial centered at x=2 for some function f, how do you estimate the value of f'(1.9)?
  
• Question #f639b
  
• How is a type 1 error more dangerous than a type 2 error in statistics?
  
• What are the extrema and saddle points of `f(x, y) = xy(1-x-y)`?
  
• What are the absolute extreme values of the function `f(x) = x/sqrt(x^2+1)` on the interval `[0,2]`?
  
• D is matrix of order `n*n` such that `D=Diag[d_1,d_2,.....d_n]` find f(D)?
  
• What are the removable and non-removable discontinuities, if any, of `f(x)=(x+3)/((x-4)(x+3))`?
  
• What is the net area between `f(x)=(x-x^2)/ln(x^2)` in `x in[1,2]` and the x-axis?
  
• Question #b15b8
  
• In the limit `lim_(t to oo) 1/(1+4t)=0` , how do you find `B>0` such that whenever `t>B`, `1/(1+4t)<0.01`?
  
• How do you factor `6x ^ { 3} + 2x ^ { 2} - 3x - 1`?
  
• Question #e6cad
  
• How do you find a power series converging to `f(x)=int ln(1+t^2) dt` from [0,x] and determine the radius of convergence?
  
• How do you find the intervals of increasing and decreasing using the first derivative given `y=sinx+cosx`?
  
• What is the equation of the line normal to `f(x)=lnx^2-1/x^2` at `x=-2`?
  
• Why is it impossible to have `lim_(x->0) f(x)` and `lim_(f(x)->0)f(x)` simultaneously exist for any of these graphs?
  
• How do you solve `3000/(2+e^(2x))=2`?
  
• If f(x) and g(x) are functions such that `f(3)=2, f'(3)=1,g(3)=0,` and `g'(3)=4`. What is `h'(3)`, where `h(x)= (f(x) +g(x))^2`?
  
• How do you find the equations for the tangent plane to the surface `g(x,y)=x^2-y^2` through (5,4,9)?
  
• How do you evaluate `\sqrt { 25} - 9\cdot 2^ { 3}`?
  
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