Answers created by Sasha P.

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• Question #3ef80
  
• Question #fefc1
  
• A triangle has sides A, B, and C. The angle between sides A and B is #(pi)/6#. If side C has a length of #1 # and the angle between sides B and C is #(7pi)/12#, what are the lengths of sides A and B?
  
• Question #f80ea
  
• How do you express #\frac { 1} { 2} \log _ { c } x + 3\log _ { c } y - 5\log _ { c } x# as a single logarithm?
  
• How do you write a polynomial equation of least degree given the roots 6, 2i, -2i, i, -i?
  
• How do you find the equations for the normal line to #x^2+y^2=20# through (2,4)?
  
• We have #f:RR->RR,f(x)=|x|root(3)(1-x^2)#.Is this function continous in #x=0#?
  
• Question #9abc1
  
• How do you differentiate #f(x) = (e^(4-x))/(e^(1-x)-1)# using the quotient rule?
  
• Let R be the region in the first quadrant bounded by the graphs of #y=x^2#, #y=0#, and #x=2#, how do you find the area of R?
  
• How do you find the derivative of #R(w)=w^3*cos(4w)#?
  
• Question #9ff05
  
• What is the equation of the tangent line of #f(x) =(4x) / (3-4x^2-x) # at # x = 1#?
  
• Question #495d2
  
• How do you differentiate #sin(arctan x)#?
  
• # lim_(n->oo)(1+1/n)^n = # ?
  
• How do you find the equation of the line tangent to #y=x^3# at the point (-1,-1)?
  
• How do you find the slope of a tangent line to the graph of the function #f(x)=x^3-2x+1# at (2,5)?
  
• How do you integrate #f(x)=(-x^2-2x)/((x^2+2)(x+7))# using partial fractions?
  
• How do you find the indefinite integral of #int (3x^-2-4x^-3)dx#?
  
• What is the equation of the normal line of #f(x)=5x^3+2x^2+x-2# at #x=2#?
  
• What is the derivative of #f(x) = 2 tan^(2)x-sec^(2)x#?
  
• How do you differentiate #h(x)=3e^sin(x+2)#?
  
• How do you find the derivative of #xsqrt(2x - 3)#?
  
• What is the equation of the line tangent to #f(x)=2x ^3+8x # at #x=1#?
  
• How do you find sum of geometric series 2+6+18+...+1458?
  
• How do you use Heron's formula to determine the area of a triangle with sides of that are 4, 6, and 8 units in length?
  
• What is the distance between the following polar coordinates?: # (6,(7pi)/12), (2,(-3pi)/8) #
  
• How do you find the derivative of #r(x)= (0.3x^2-4.2x+9.2)^1.5#?
  
• How do you differentiate # e^x/ln x#?
  
• A ski club with 28 members went on a ski trip. Some members rented skis and the rent for $16.00 a day and snowboards rent for $19.00 a day, and the club spent $478.00 in rentals, how many ski club members rented skis?
  
• If #A= <2 ,6 ,-3 ># and #B= <-6 ,-4 ,4 >#, what is #A*B -||A|| ||B||#?
  
• What is the equation of the tangent line of #f(x)=x^2e^(x-2)-xe^x# at #x=4#?
  
• What is the derivative of #sqrt(3x+1)#?
  
• How do you differentiate #f(x) = e^(e^x)#?
  
• How do you differentiate #f(x)= (x^2+1)(x^3+1) # using the product rule?
  
• What is the equation of the normal line of #f(x)= e^(x^2/(x-2))# at #x = 3#?
  
• How do you find #int (x-1)/((x^3+1))dx# using partial fractions?
  
• How do you differentiate #f(x)=ln(1/sin(3x))# using the chain rule?
  
• How do you find #int (7x^2+x-1) / ((2x+1) (x^2-4x+4)) dx# using partial fractions?
  
• What is #int ln(lnx)/x dx#?
  
• How do you differentiate #f(x)=4x ln(3sin^2x^2 + 2)# using the chain rule?
  
• What is #int (e^(ix)-e^(-ix))/(2i)dx#?
  
• How do you integrate #int (3-x)/((x^2+3)(x+3)) dx# using partial fractions?
  
• How do you find the integral of #f(x)=x^5lnx# using integration by parts?
  
• What is the derivative of # e^cosx + cos(e^x)#?
  
• How do you find the derivative of # f(t)=sin^2[e^(sin^2)t]# using the chain rule?
  
• How do you find #int 2/((x^4-1)x) dx# using partial fractions?
  
• How do you differentiate #f(x)=x^6/e^(x-6)# using the quotient rule?
  
• How do you differentiate #f(x)=e^tan(lnx)# using the chain rule?
  
• How do I find the derivative of #F(x)=arcsin(sqrtsinx)#?
  
• What is the derivative of #f(x) = cos( sin( x ))#?
  
• How do you find the arc length of the cardioid #r = 1+cos(theta)# from 0 to 2pi?
  
• How do you find region bounded by circle r = 3cosΘ and the cardioid r = 1 + cosΘ?
  
• How do you find the integral of #int cotx dx#?
  
• How do you find the area of the region shared by the circles #r=2cos(theta)# and #r=2sin(theta)#?
  
• How do you use partial fraction decomposition to decompose the fraction to integrate #1/((x+2)(x^2+4))#?
  
• How do you determine whether a linear system has one solution, many solutions, or no solution when given 3x-2y= 10 and -6x +4y= -20?
  
• Is the derivative of #sin^3[x] 3sin^2[x] (cos^3[x])#?
  
• How do you find f'(x) using the definition of a derivative for #f(x)=cos x#?
  
• How do you differentiate #y=(4/ln2)(x^(lnx))(lnx+2ln(cosx))#?
  
• How do you integrate #int ( 6x^3+3x+sqrt7 ) sin( 5x ) dx#?
  
• How do you find the derivative of #f(x)=1/(x-1) #?
  
• How do you use the Intermediate Value Theorem to show that the polynomial function #f(x) = x^4 + 8x^3 - x^2 + 2# has a zero in the interval [-1, 1]?
  
• How do you find the derivative for #(3x+1)^4(2x-3)^3#?
  
• How do use the first derivative test to determine the local extrema #y = (x^2 + 2) /( x^2 + 1)#?
  
• How do you find the derivative of #cos 5x#?
  
• What is the limit of # (2x^2-4x) / (x+1)# as x goes to infinity?
  
• Question #aa3b8
  
• How do I find the sum of the series: 4+5+6+8+9+10+12+13+14+⋯+168+169+170. since D is changing from +1, +1 to +2 ?
  
• How do you integrate #ydx = 2(x+y)dy#?
  
• How do you find the integral of #int arctan(x) dx#?
  
• How do you find the integral of #int (sin x)/(cos^2x + 1)dx#?
  
• How do you find the integral of #int (6sin^6x)(cos^3x)dx#?
  
• How do you find f'(x) using the definition of a derivative for #f(x)=(4/x^2) #?
  
• How do you find the integral of #int [arccos(x)]^n# if is an integer?
  
• What is the derivative of #ln( secx+tanx)#?
  
• How do you determine whether the function #f(x) = x/(x^2 - 5)# is concave up or concave down and its intervals?
  
• How do you use the Intermediate Value Theorem to show that the polynomial function # 2x^3 + x^2 +2# has a root in the interval [-2, -1]?
  
• How do you use the ratio test to test the convergence of the series #∑ 3^n/(4n³+5)# from n=1 to infinity?
  
• How do you differentiate #(4x^-2) - 8x + 1#?
  
• What is the limit of # f(x) = (2x+5)/abs(3x-4)# as x goes to infinity?
  
• What is the derivative of #y=log_x 3#?
  
• How do you integrate #int4x(x^2+3)^(-3) dx#?
  
• How do you find the derivative of #3/2 t^(1/2)#?
  
• How do you find the integral #ln(x^2+4)#?
  
• How do you find the volume of the region bounded b the line #y = x-2#, the x-axis, #x=2#, and #x=4# is revolved about the line #x = -1#?
  
• How do you find the volume of the torus formed by revolving #(x-2)^2 +y^2=1# about the y-axis?
  
• How do you find the indefinite integral of #int (5x^2 – 4x + 7)/((x^2+1)(2x – 1)) dx#?
  
• How do you find the limit of #1/(x-1)# as x approaches 1?
  
• How do you find f'(x) using the definition of a derivative for #f(x)= 5x + 9 # at x=2?
  
• How do you find the integral of #1/tan(x) dx#?
  
• How do you find the integral of #int cos x * tan x dx#?
  
• How do you use the ratio test to test the convergence of the series #∑ (-5)^(n+1)n / 2^n# from n=1 to infinity?
  
• How do you find the derivative of #y=4x^(-1/4)-5+sqrt(3x)#?
  
• What is the limit of #x^2e^x# as x goes to infinity?
  
• What is the derivative of #ln(2x^2+1)#?
  
• What is the derivative of #y=ln[x/(2x+3)]^(1/2)#?
  
• How do you find the equation of a line tangent to a graph #z = sqrt (60 - x^2 - 2y^2)# at the point (3, 5, 1)?
  
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