Answers edited by Steve M

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• How do you integrate #int x/sqrt(2+3x)# by parts?
  
• How to you find the general solution of #dy/dx=xsqrt(5-x)#?
  
• How do you find the derivative of #f(x)=x^3+x^2# using the limit process?
  
• How do you integrate #ln(x)/x^3#?
  
• What is the derivative of this function #y= (1+sin x)/(1-sin x)#?
  
• What is the derivative of # ln[-30(x^3-2x+e^x)^5]#?
  
• How do you find the derivative of #y=ln((x-1)/(x+1))^(1/3)#?
  
• Is #f(x) =e^x/x-x^3-3# concave or convex at #x=-1#?
  
• How do you find the points where the graph of the function #y=(x+3)(x-3)# has horizontal tangents?
  
• How do you integrate #y=sinx/tanx# using the quotient rule?
  
• What is the solution to the Differential Equation #dy/dx = sin(x+y) + cos(x+y)#?
  
• How do you find #(d^2y)/(dx^2)# for #5x^2=5y^2+4#?
  
• How do you find the limit of #x/sinx# as x approaches 0?
  
• What is the derivative of #x^(lnx)#?
  
• How do you integrate #secx^4 dx#?
  
• How do you find the inner product and state whether the vectors are perpendicular given #<3,1,4>*<2,8,-2>#?
  
• A coin is dropped from a height of 750 feet. The height, *s* (ft), at time *t* (sec), is given by #s=-16t^2+750#. How long does it take for the coin to hit the ground?
  
• How do you prove that the limit of #(x^2+3x)=-18# as x approaches -3 using the epsilon delta proof?
  
• How do you use the first and second derivatives to sketch #y= -(x-2) (x+2) (x-4)#?
  
• What is the derivative of #sec(x-x^2)#?
  
• How do you find the maximum value of # y = -x^2 + 8x - 4#?
  
• How do you find the slope of the line tangent to the graph of #y = x ln x# at the point ( 1,0 )?
  
• Prove that? # lim_(h->0)(sec(x+h) - sec x)/h = sec x*tan x #
  
• What is the slope of the line normal to the tangent line of #f(x) = e^(x^2-1)+3x-2 # at # x= 1 #?
  
• How do you integrate #int 1/(2x^3)dx#?
  
• How do you find the equation of the tangent line to the curve #y=x^4+2x^2-x# at (1,2)?
  
• How do you use the definition of a derivative to find the derivative of # f(x) = 5x + 9# at x=2?
  
• How do you find the equation of the tangent lines to the curve at the point x=2 considering the equation #x^2-2xy+4y^2=64#?
  
• Find the derivative of #sinx# using First Principles?
  
• How do you find the derivative of #5=3e^(xy)+x^2y+xy^2#?
  
• How do you integrate #(x - 16) / (x^2 + x - 2)# using partial fractions?
  
• How do you find the limit of #x/sinx# as x approaches 0?
  
• What is a solution to the differential equation #dy/dx=e^(x+y)#?
  
• Question #c4080
  
• How do you compute the 9th derivative of: #arctan((x^3)/2)# at x=0 using a maclaurin series?
  
• Using the limit definition, how do you differentiate #f(x) =1/(x+2)#?
  
• How do you find intercepts, extrema, points of inflections, asymptotes and graph #y=(20x)/(x^2+1)-1/x#?
  
• For #f(t)= (t^2,t^3)# what is the distance between #f(1)# and #f(3)#?
  
• How do you find ((d^2)y)/(dx^2)?
  
• How do you use the limit definition of the derivative to find the derivative of #f(x)=-4x^3-3x^2+1#?
  
• What are the asymptotes of #f(x)=-x/((x^2-8)(x-2)) #?
  
• If #g(x)=x/(e^x)#, what is #g^(n) (x)#?
  
• How do you evaluate the definite integral #int e^x# from #[0,ln2]#?
  
• How do you find the limit of #x/sinx# as x approaches 0?
  
• A tangent line is drawn to the hyperbola #xy=c# at a point P, how do you show that the midpoint of the line segment cut from this tangent line by the coordinate axes is P?
  
• How do you find #(dy)/(dx)# given #x^2+y^2=1#?
  
• How do you find the area bounded by #y=x+4# and #y=x^2+2#?
  
• How do you integrate by substitution #int x^2(x^3+5)^4 dx#?
  
• What is a solution to the differential equation #y'' + 4y = 8sin2t#?
  
• Differential Calculus Word Problem?
  
• How do you find the derivative of #f(x) = 2/(x-1) - 1/(x+2) #?
  
• Prove that #secx-cosx=tanxsinx#?
  
• What is the acceleration of the system and the tension in the ropes joining the masses in the following diagram?
  
• Is #f(x) = (x+3)^(2/3) - 6# concave or convex?
  
• How do you find the limit of #(2-e^x)/(2+3e^x)# as x approaches infinity?
  
• What is the equation of the normal line of #f(x)=e^-x+x^3# at #x=-5#?
  
• How do you find the equation of the tangent and normal line to the curve #y=x^2-x# at x=1?
  
• How do you find the limit of #sinx/(x-pi)# as #x->pi#?
  
• How do you use the properties of summation to evaluate the sum of #Sigma (i^2-1)# from i=1 to 10?
  
• How do you find the limit of #(x^2-4)/(x-2)# as x approaches 2?
  
• How do you find #(dy)/(dx)# given #xe^siny=e^y#?
  
• Question #ae2f4
  
• How do you calculate #(d^2y)/(dx^2)# of #y=-4x^2+7x#?
  
• How do you use the chain rule to differentiate #y=5tan^5(2x+1)#?
  
• How do you differentiate #y=e^(e^x)#?
  
• How do you find #(dy)/(dx)# given #xe^siny=e^y#?
  
• How do you use the limit definition to find the derivative of #y=-4x-5#?
  
• How do we find the values of k and m that makes function continue anywhere piecewise function of #(x^2) + 5# when x > 2, #m(x+3) + k# when #-1 < x <=2# and #2(x^3) + x + 7# when #x <=-1#?
  
• How do you use the limit definition to find the derivative of #f(x)=(4-3x)/(2+x)#?
  
• How do you find the critical numbers of #f(x)= 2x^3 + 3x^2-12x#?
  
• How do you simplify #(n+4)(n+5)(n+3)!#?
  
• How do you solve #4cos^2x-1=0#?
  
• What types of points are critical points?
  
• How do you determine where the function is increasing or decreasing, and determine where relative maxima and minima occur for # f(x) = sqrt(x^2+1) #?
  
• How do you find the antiderivative of #int (xe^x) dx#?
  
• How do you find the derivative of #ln(x^3+3x)#?
  
• How do you use a power series to approximate # int_0^1xtan^-1xdx #?
  
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