Recent content by Kenji Liew

  1. K

    Undergrad Why L' Hospital's rule cannot apply directly for sequence

    Thanks for your prompt reply. I think I can understand after looking at your explanation.
  2. K

    Undergrad Why L' Hospital's rule cannot apply directly for sequence

    Homework Statement Well, this thread is purposely to clarify my question on the use of L'Hospital's rule for sequence. As I have read from the calculus book, the sequence can be defined such that f:N → ℝ with function f(n)= an where n inside natural numbers,N. So, we cannot apply L'...
  3. K

    Derivative of Composite Function

    Thank you for the reply. I got the idea from it. This is because my lecturer want us to compare whether the answer obtained from directly differentiate h(x) is the same as the answer obtained from the chain rule. :smile:
  4. K

    Derivative of Composite Function

    Homework Statement \begin{equation} f(x)= \begin{cases} 5x+2 &, x \leq 1 \\ 3x^2 &, 1<x<2\\ 4-x &, x\geq 2 \end{cases} \end{equation} \begin{equation} g(x)= \begin{cases} \frac{1}{5}(2+3 cos x) &, x <0 \\ 4-sin x &, x \geq 0 \end{cases} \end{equation} Find h = f...
  5. K

    Mathematica Mathematica: Change the data from column to row

    Thanks, it worked!
  6. K

    Mathematica Mathematica: Change the data from column to row

    Hi, I have put my data in column form ( a large number of data) in Notepad. I have attached example of the data. I know how to import it into Mathematica. However I face the problem to change the whole set of data to row form in Mathematica so that I can plot the histogram in Mathematica. Thanks.
  7. K

    Integration Problem: Solve Inte[x]sqrt[1+e^(2x)]dx

    Thanks as well, dextercioby for the another method !
  8. K

    Integration Problem: Solve Inte[x]sqrt[1+e^(2x)]dx

    Thanks for your help,Vela ! :smile::smile:
  9. K

    Integration Problem: Solve Inte[x]sqrt[1+e^(2x)]dx

    I have attached the reply in PDF
  10. K

    Integration Problem: Solve Inte[x]sqrt[1+e^(2x)]dx

    I am very sorry.I have a typo in the question and just done the correction.
  11. K

    Integration Problem: Solve Inte[x]sqrt[1+e^(2x)]dx

    Homework Statement \inte^{x}\sqrt{1+e^{2 x}}dxHomework Equations Cosh x = [ e^{x}+ e^{-x} ] / 2 The Attempt at a Solution \inte^{x}\sqrt{1+e^{2x}}dx = \inte^{x}\sqrt{2e^{x}Cosh x}dx I have no idea on how to proceed already. I cannot obtained the solution given by Mathematica. I use...
  12. K

    Finding limit using L'Hospital rule

    May be the lecturer try to test the students understanding.:smile:
  13. K

    Finding limit using L'Hospital rule

    Thanks for replying.I think something wrong with this question.
  14. K

    Finding limit using L'Hospital rule

    Hi, I am facing problem on solving this question. Homework Statement Given limx\rightarrow\infty(3x2+1)x Homework Equations From the above limit, if we substitute x\rightarrow\infty, obviously we don't have the indeterminate forms: \infty^0 , 00 or 1\infty. The Attempt at a Solution...
  15. K

    Graduate Need Help in Direct Product and Quotient (factor) Group

    Hi All. I have several questions on abstract algebra. Here are my questions and the attempts I had done so far. (1)Let denote Z as the integer.According to theorem, the direct product of Z3 X Z7 = Z21. Hence, is Z4 X Z2 is equal to Z8? Z2X Z2 is equal to Z4? (2)For Z4 ={0,1,2,3 }, and Z2...