Answers created by Roy E.

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• What is the integral of `int ln x / x dx`?
  
• How does calculus relate to physics?
  
• Can the ozone layer repair itself?
  
• How do you find the area of the parallelogram with vertices: p(0,0,0), q(-5,0,4), r(-5,1,2), s(-10,1,6)?
  
• Can somebody please explain to me the signs used for ∂m in this solution, with regard to the 'u'. I do not understand why '-|∂m|' is used, and then how it is later changed to a '+∂m'? Thanks in advance!
  
• Can somebody please explain to me the signs used for ∂m in this solution, with regard to the 'u'. I do not understand why '-|∂m|' is used, and then how it is later changed to a '+∂m'? Thanks in advance!
  
• What the derivative of lnx?
  
• Can someone please explain what is going on here?
  
• How do you find the points of inflection of the curve `y=e^(x^2)`?
  
• How do you use Integration by Substitution to find `intx/(x^2+1)dx`?
  
• Hi everyone, I am having difficulty in getting the correct answer for some reason. Can someone assist me and explain how to do this properly?
  
• I heard that because of global warming it is going to be really hot (or cold), and way sooner than expected - is that true?
  
• Evaluate `int(x^6+1)/(x^2+1)dx` ?
  
• Evaluate `int(x^6+1)/(x^2+1)dx` ?
  
• Derivative of `e^x-e^-x`?
  
• How do you factor the expression `3x^2 - 6x - 9`?
  
• How do I write the relationship between m and n?
  
• What is green house effect and global warming??
  
• How do you find the distance between (3,-5), (-3,0)?
  
• How do you find the sum of the finite geometric sequence of `Sigma 2(-1/4)^n` from n=0 to 40?
  
• Evaluate the limit. Be sure to show your reasoning. limit as x approaches 0 (sin7x / tan3x) ?
  
• Find the points on the curve y=2x^3-9x^2+42 where the tangent like is horizontal?
  
• The three hydrogen atoms and one nitrogen atom in an ammonia molecule form a tetrahedron—a pyramid with four triangular faces. Three of these faces are isosceles triangles with the nitrogen atom at the vertex. If the distance between the hydrogen...?
  
• How do you simplify `sin 15° cos 75° + cos 15° sin 75°`?
  
• How and when did the ozone layer form?
  
• Weight of object at earth surface is 10 kg. Find the weight of object at the centre of earth?
  
• Can you evaluate the integral by interpreting it in terms of areas?
  
• What is the most abundant greenhouse gas in our atmosphere?
  
• Question #bc921
  
• Question #7217e
  
• How is ozone formed in the stratosphere?
  
• How do you use the first and second derivatives to sketch `g(x)= ( 1 + x^2 ) / ( 1 - x^2 )`?
  
• What experiments are scientists doing about global warming?
  
• Question #f33e6
  
• Question #9faa3
  
• Where does most of the oil that pollutes the ocean come from?
  
• Question #01141
  
• A rectangular trampoline has an area of 187 square feet. The length of the trampoline is 17 feet. What is its width?
  
• How do you integrate `int (x-1)/( x^4 (x-1)^2)` using partial fractions?
  
• How did the ozone layer form?
  
• What is the axis of symmetry and vertex for the graph `y=-3(x+6)^2+1`?
  
• How do you integrate `int (x^3)/(x^2 + 8x + 16)` using partial fractions?
  
• How do you find the indefinite integral of `int (2x)/(x-1)^2`?
  
• What is `f(x) = int -cos^2x dx` if `f(pi/3) = 0`?
  
• How do you use linear approximation to the square root function to estimate square roots `sqrt 3.60`?
  
• How do you find the sum of the infinite geometric series `1/8+1/32+1/128+...`?
  
• How do you graph `f(x)=(x-2)/(x^2-5x-6)`?
  
• How do you find the nth derivative of the function `f(x)=x^n`?
  
• How do you integrate by substitution `int x/(sqrt(1-x^2) dx`?
  
• How do you identify the center and radius of the circle `x^2+y^2=1`?
  
• How do you integrate `int root3(x^2)dx`?
  
• What is the graph of `r=a cos 6theta`?
  
• How do you find the exact value of `3lne^4`?
  
• How do you find the equation of a parabola with vertex at the origin and directrix x=-2?
  
• Is .5287593593593 rational or irrational?
  
• Given `(x - 4) / (x^2 - 2x - 8)` how do you find the limit as x approaches -2?
  
• How do you solve the system `9x - 18y + 20z = -40` `29x - 58y + 64= -128`, `10x - 20y + 21z = -42`?
  
• Question #57ce5
  
• How do you integrate `int cos^2x` by integration by parts method?
  
• How do you find the volume of the solid bounded by the coordinate planes and the plane `2x+y+z=3`?
  
• How do you evaluate `arcsin(sin3pi)` without a calculator?
  
• Question #603e4
  
• What does `(x-4)^2/4+(y-7)^2/9=1` represent?
  
• How do you find the coefficients in the row of Pascal's triangle corresponding to n=8?
  
• How are certain formulæ for areas of circles and ellipses related to calculus?
  
• How do you prove that the circumference of a circle is `2pir`?
  
• How do you use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson’s Rule to approximate the given integral `(1+​cos(​x))^​(1/3)` from #[pi/2,0]?
  
• Question #5b598
  
• How do you evaluate `e^( ( 23 pi)/12 i) - e^( ( 17 pi)/12 i)` using trigonometric functions?
  
• How do you evaluate `log_(1/13) (1/169)`?
  
• Question #59543
  
• Question #ba4a6
  
• Question #ba4a6
  
• Why do optical isomers rotate polarized light?
  
• How do you use the differential equation `dy/dx=-48/(3x+5)^3` to find the equation of the function given point (-1,3)?
  
• How do you integrate `int (x^2-2x+1)/(x-2)^3` using partial fractions?
  
• How do you integrate `int (x^3-x^2)/ (x+3)^4` using partial fractions?
  
• How do you use partial fractions to find the integral `int (x^2+x+3)/(x^4+6x^2+9)dx`?
  
• How do you find the Vertical, Horizontal, and Oblique Asymptote given `(x^2-64)/(x-8)`?
  
• How do you solve the quadratic using the quadratic formula given `3a^2=6a-3`?
  
• How do you expand `(p+q)^5`?
  
• How do you integrate `int x(x+1)^8` using substitution?
  
• How do you find the integral of `cos^n x`?
  
• What are the local extrema of `f(x)= x^3 - 3x^2 - x + 1`?
  
• How do you solve `1/x+2/3=2` and check for extraneous solutions?
  
• How do you write a polynomial function with the given zeros 1, –2, and 5?
  
• How do you evaluate `x / sqrt (4x^2 + 2x +1)` as x approaches negative infinity?
  
• Whats a two letter word with a C in it? for scrabble?
  
• How do you integrate `f(x)=x/(x^2+1)` using the quotient rule?
  
• An object with a mass of `24 kg` is hanging from an axle with a radius of `14 m`. If the wheel attached to the axle has a radius of `42 m`, how much force must be applied to the wheel to keep the object from falling?
  
• Question #27ac2
  
• Question #b9556
  
• How do you evaluate the limit `(4^x-1)/(8^x-1)` as x approaches `0`?
  
• Why are biofuels important in transportation?
  
• How to you find the general solution of `dy/dx=x/y`?
  
• Question #d1bd3
  
• Question #43b93
  
• What is the probability of rolling a sum of 10 with two dice?
  
• How do you find the fourth root of `-8 + 8sqrt3i`?
  
• What is the square root of -49?
  
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