MATH3503 Online Assignment 1

• Make sure to use the link on the Learning Hub, which contains a user name and a user ID unique to you, otherwise your mark would not be recorded. You may use the URL without '?uname=...&uid=...' if you just want to practice. You will get different numbers every time you open the page.
• Numerical answers are evaluated as correct if the difference from the correct value is less than `0.001 times` (correct value) unless otherwise specified. That means, you need to keep at least 4 significant digits (e.g., 12.34, 0.01234, etc.) in your final answer, and a couple of more digits in the intermediate steps.
• Arithmetic operators:

  Multiplication	* (You cannot omit it!)
  division	/

  Available functions

  • Trigonometric functions: sin(x), cos(x), tan(x), sec(x)
  • Exponential and logarithmic functions with base e: exp(x) (`=e^x`), ln(x) (or log(x))
  • Square root: sqrt(x)

  1. Derivatives and Integrals

  1. 1.   `d/(dx)(x^{6})=`
     2.   `(dy)/(dx) = x^{5}`  `leftrightarrow`  `y=int x^{5} dx =``+C`
  2. 1.   `d/(dx)(x^{-7})=`
     2.   `(dy)/(dx) = x^{-8}`  `leftrightarrow`  `y=int x^{-8} dx =``+C`
  3. 1.   `d/(dx)((7x+5)^{5})=`
     2.   `(dy)/(dx) = (7x+5)^{4}`  `leftrightarrow`  `y=int (7x+5)^{4} dx =``+C`
        * Do not expand the integrand.
  4. 1.   `d/(dx)(x^{19/17})=`
     2.   `(dy)/(dx) = x^{2/17}`  `leftrightarrow`  `y=int x^{2/17} dx =``+C`
  5. 1.   \(\displaystyle\int(7x^{11}+10x^{-3} +6x^{1/4}-7\sqrt[12]{x^{2}})dx\)
        `=``+C`
        Hint: Express the radical in exponential notation.
     2.   \(\displaystyle\int (7x+11)^{-19/5} dx =\)`+C`
        Hint: The derivative of the answer is the integrand (the function to be integrated).
  6. 1.   `d/(dx)sin(7x)=`
     2.   `(dy)/(dx) = cos(7x)`  `leftrightarrow`  `y=int cos(7x) dx =` `+C`
  7. 1.   `d/(dx)cos(9x)=`
     2.   `(dy)/(dx) = sin(9x)`  `leftrightarrow`  `y=int sin(9x) dx =` `+C`
  8. 1.   `d/(dx)tan(9x)=`
        Hint: `(tan x)' = sec^2 x = 1/cos^2 x`. Enter `cos^2 x` as cos(x)^2
     2.   `(dy)/(dx) = 1/(cos^2(9x))`  `leftrightarrow`  `y=int dx/(cos^2(9x)) =` `+C`
  9.  
     `int(9sin(3t)+6cos(3t))dt =` `+C`
     
  10. 1.   `d/(dx)e^{-4x}=`
         Enter `e^x` as exp(x)
      2.   `(dy)/(dx) = e^{-4x}`  `leftrightarrow`  `y=int e^{-4x} dx =` `+C`
  11.  
      `int(2e^{9t+4}+5e^{-9t+4})dt =` `+C`
      
  12. 1.   `d/(dx)ln(7x)=`
         
      2.   `(dy)/(dx) = 7/x`  `leftrightarrow`  `y=int\ 7/x dx =` `+C`
         Enter `ln x` as ln(x), `|x|` as abs(x)
  13.  
      `int(2/(x+8)+9/(4x-5))dx =` `+C`
      

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