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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