Answers created by Jim H

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• Use the definition of limit to prove the following limit lim x->-3 (x^2+4x+1)=-2 in epsilon delta? .
  
• What is the derivative of sin2(x) by first principle? Please note I know the chain rule (and can pretty much get the correct answer through that)
  
• What is an example of long division of polynomials?
  
• How do you find the slope of the secant lines of `f(x) = 2/x + 2` through the points: (0, f(0)) and (0+h, f(0+h))?
  
• How to solve this integral `int 3/(x+1)^2 sqrt((x-1)/(x+1)) \ dx`?
  
• Can you help me with this double integral?
  
• Can you help me with this double integral?
  
• can you help me with this double integral?
  
• What is the next term in the sequence?: 3,6,12,21,33, ...
  
• What is the area between two lines?
  
• `lim_(x->0)sin(1/x)/(sin(1/x))` ?
  
• How to do these question?
  
• How to do this question?
  
• How do you find the area between `y^2=-4(x-1)` and `y^2=-2(x-2)`?
  
• How do you use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by `y^2=8x` and x=2 revolved about the x=4?
  
• How to increase accuracy of trapezoidal and simpson rule in calculus?
  
• Is (3,4),(5,4),(1,3),(4,1),(9,4) a function?
  
• Find the area of the shaded region?
  
• In the expression 6x, x is what?
  
• For what values of x, if any, does `f(x) = 1/(x^2-2x+1)` have vertical asymptotes?
  
• Use Rolle's theorem to prove that the equation x^3 -15x + c = 0 has no more than one root in the interval [-2, 2] ?
  
• Find initial position via intergration???
  
• For example, f(x) is a multipart which if divided by `x^3+27`, the remainder is `x^2-2x+7`. If f(x) is divided by `x^2-3x+9`, the remainder is?
  
• How do you find intercepts, extrema, points of inflections, asymptotes and graph `f(x)=x/sqrt(x^2+7)`?
  
• How do we show that this is true?
  
• How do you determine the limit of `(x-pi/2)tan(x)` as x approaches pi/2?
  
• What is the slope of the tangent line of `(x+2y)^2/(e^(x-y^2)) =C`, where C is an arbitrary constant, at `(1,1)`?
  
• F(x)=secx tanx/sinx ?
  
• Change the order of integration and evaluate?
  
• Given the function f defined by f(x) =(2x-2)/(x^2+x-2) for what values of x is f(x) discontinuous?
  
• How do you find the slope of the tangent line at point (2, 1) for `y=(x^2+1)`?
  
• What is the Integral of y-2ye^x with respect to x?
  
• Limit x tends to infinity ((x+1)(x+2)(x+3))^1/3-x=?
  
• What is the implicit derivative of `5=x-1/(xy^2)`?
  
• How do you find the surface area generated when the curve `y=sqrt(r^2-x^2), 0<=x<=a` is rotated about the x axis?
  
• How can integrate this? `int_-∞ ^∞(e ^(-4t) ) dt`
  
• Approximate `\int_0^2(1)/(1+x^3)dx` using the Midpoint Rule, given `n=4`? Please check my work
  
• How do I know if a discontinuity in a function is removable or not?
  
• Calc 2 Problem. Could someone help me understand the "u" notation in this integral?
  
• Consider the function 1-7x^2 on the interval [-2, 7]. How do I find the average slope on this interval? Find the one point in which f'(c) is equal to the mean slope.
  
• What does limit does not exist mean?
  
• `lim_(t->-oo) sqrt(t^2+2t+7 ) -sqrt(t^2-2t+5)`=?
  
• Please help me with Lim excercise and explain it as well? Really appreciate!
  
• What is the square root of (-12)^2?
  
• Can someone explain the steps 3 and 4 please? Thanks a lot <3
  
• If the first derivative has a cusp at x=3, is there a point of inflection at x=3 even though the second derivative doesn't exist there?
  
• If `y=(x^3)ln(x^3)` then `dy/dx=`?
  
• What is the derivative of `f(x)=1/(sin^2x+cos^2x)`?
  
• How would I graph x > -2 on a coordinate plane?
  
• How do you find the volume of a solid of revolution using the disk method for `y= 3/(x+1)`, `y=0`, `x=0`, `x=8` revolved about the `x`-axis?
  
• Is this true or false? `sin^2(θ) ≠ sin(θ)^2`
  
• A ladder 10ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a speed of 2ft/s, how fast is the angle between the top of the ladder and the wall changing when the angle is `pi/4` rad?
  
• How do you factorise 21xy-3x-28y+4 ?
  
• What is the opposite of exponential growth?
  
• Does anyone understand this? Find [f ○ (g ○ h)](2) if f(x) = 2x - 1, g(x) = 4x, and h(x) = x2+ 1. ??
  
• Why does integration by parts work?
  
• Is it possible to solve this integrate by integrate substitution method?
  
• What is 19 over 25 as a decimal?
  
• Is it possible to solve this integrate by integrate substitution method?
  
• What is the average value of the function f(x)=3x^2-4 on the [2,6]?
  
• Multiple Choice question: why is the answer B? I would think it's C.
  
• The amount of a certain drug present in a patient's body t days after it has been administered is C(t)=5e^-0.2t Determine the average amount of drug present in the patients body for the first 4 days after drug is administered. Help?
  
• How to find these type of question easily, without using L-hopitals rule?
  
• What's the integral of `int cos^2(x) tan^3(x) dx`?
  
• What is multivariable calculus?
  
• If csc(ϴ) = 6, find the exact value if sin(2 ϴ)?
  
• Help me to find it please? I am studying for my midterm in real analysis and I got problem in it.
  
• Find value(s) c ∈ (−2, 4) such that f'(c) is parallel to the chord line joining ?
  
• What are the maximum and minimum values of the function `abs(2x-3` at closed intervals [1,2]?
  
• What are the maximum and minimum values of the function `abs(2x-3` at closed intervals [1,2]?
  
• Limxtends to infinityx/modulus of x..?
  
• How many combinations can you make with the numbers 1,2,3?
  
• Which value of c satisfies the conclusion of the mvt for the function f(x)=7x^2+3x+7 on the interval [-3,3]?
  
• What is inverse variation?
  
• Is this right? ∫(dx)²=∫2dx
  
• Is it true that Dividend over Divisor = Quotient + Remainder?
  
• How do you place the inclusion symbols to make the statement `3*4+2`/`6=3` true?
  
• Find the limit?
  
• Can you determine the equation of the tangent line of a point on a function by solely using the function's graph?
  
• How do you find the volume by rotating region R about the x-axis?
  
• I really need help. It's about number theory. Would yo be so kind help me?
  
• How do you find the arc length of the curve `y=xsinx` over the interval [0,pi]?
  
• What is the shortest distance from the point `(-3,3)` to the curve `y=(x-3)^3`?
  
• Method of substitution is used. Step-by-step solution is requested. How do we integrate when u = [ 1 - sin( x ) ]?
  
• Integration of [X+[x+[x]]] at limit -1 to 1 ?
  
• Show that `f` is not constant and find `f`?
  
• How do you find the slope of a tangent line to the graph of the function `F(t)= 3- (8/3t)` at point: (2/4, -7/3)?
  
• How do I solve this limit? `lim_(x->0)((1-cos^3(3x))/(xsin6x))`
  
• Why does a sum using the difference method need to factorise out common factors?
  
• A series of integral based questions?
  
• Right the equation of least degree given the roots. what is the solution? x=3,-1,5
  
• I have struggles with the last part...?
  
• Find the equation of the tangent line to the curve x^2 + y^2 = (2x^2 + 2y^2 -x)^2 at the point 0, 1/2?
  
• Give example of functions f and g such that `lim_(xrarrc)[f(x)*g(x)]` exists but either `lim_(xrarrc)f(x)` or `lim_(xrarrc)g(x)` does not?
  
• What can you say about a function f defined on `RR`, periodic and growing ?
  
• Find derivative of the following function?
  
• What is the second derivative of `(f * g)(x)` if f and g are functions such that `f'(x)=g(x)` and `g'(x)=f(x)`?
  
• Which of the following are improper integrals?
  
• What is the slope of the tangent line of `(x^2-y^2)/(sqrt(4y-x)+xy) =C`, where C is an arbitrary constant, at `(1,1)`?
  
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