Answers created by Alberto P.

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• Find the sum upto infinite terms of the series: #1/(1*3) + 2/(1*3*5) + 3/(1*3*5*7) + 4/(1*3*5*7*9).......# Using partial fractions?
  
• Question #b59e0
  
• How do you graph the system of linear inequalities #4x>y# and #x<=12#?
  
• Given a circle: C(1,2) & radius #sqrt(5)# a) Find the perpendicular distance from center to #x + 2y -10=0#, show this line is a tangent to the circle. b) Find the perpendicular distance from center to #x+2y -12 =0#, show the line does not meet circle?
  
• Question #f0f5a
  
• #7cosec theta -3 cot theta =7#,then what is the value of 7#cot theta-3 cosec theta # ?
  
• Question #55de4
  
• Show that the equation #\sin(x)-6x=0# has exactly one root...?
  
• Question #9f2d8
  
• Question #eab38
  
• How do you use summation notation to write the arithmetic series #-3.9+(-1.9)+.1+...# for six terms?
  
• Question #fef44
  
• Question #039d5
  
• Question #93493
  
• Question #e7b81
  
• How do you write a polynomial of least degree with roots 4 and -7.?
  
• I need help with this cal 1 related rates question?
  
• Find the point(s) (if any) of horizontal tangent lines for the equation #x^2+xy+y^2=6#. If none exist, why?
  
• Question #2c197
  
• Question #3e769
  
• How do you graph #r=2-2costheta#?
  
• How do you prove that the limit of #x^(-1/2) = 2# as x approaches 1/4 using the epsilon delta proof?
  
• Using the definition of convergence, how do you prove that the sequence #(-1)^n/(n^3-ln(n))# converges from n=1 to infinity?
  
• How do you solve #log_10(a^2-6)>log_10a#?
  
• A triangle has corners at points A, B, and C. Side AB has a length of #48 #. The distance between the intersection of point A's angle bisector with side BC and point B is #9 #. If side AC has a length of #36 #, what is the length of side BC?
  
• How do you integrate by substitution #int(x^2-9)^3(2x)dx#?
  
• How do you integrate #int e^x/[(e^x-2)(e^(2x)+1)]dx# using partial fractions?
  
• What is the distance between the following polar coordinates?: # (6,(7pi)/12), (3,(-5pi)/8) #
  
• How do you find all local maximum and minimum points using the second derivative test given #y=tan^2x#?
  
• How do you prove that the limit of #(3x+2)=8 # as x approaches 2 using the epsilon delta proof?
  
• Using the limit definition, how do you find the derivative of # f(x) = (x^2-1) / (2x-3)#?
  
• How do you find the equations of the tangents to #5x^2-4y^2=4# at those points where the curve is cut by #5x-2y=4#?
  
• A parallelogram has sides with lengths of #16 # and #15 #. If the parallelogram's area is #8 #, what is the length of its longest diagonal?
  
• What is #f(x) = int 1/(x-3)-x/(x+4) dx# if #f(-1)=6 #?
  
• How do you find the area between #y=1/2x^3+2, y=x+1, x=0, x=2#?
  
• What is the integral of #int ( sin^3(x))dx#?
  
• Question #6c76f
  
• Question #1fcac
  
• How do you find the limit of # (x^3 - 5x^2 + 7x - 3)/(x^3 - x^2 - 5x - 3)# as x approaches 3?
  
• Two opposite sides of a parallelogram each have a length of #24 #. If one corner of the parallelogram has an angle of #( pi)/3 # and the parallelogram's area is #96 #, how long are the other two sides?
  
• How do you find the definite integral of #(x^3+x^4(tanx))dx# from #[-pi/4, pi/4]#?
  
• How do you use the limit definition to find the slope of the tangent line to the graph #f(x)= x(sqrt(x)-1) # at x=4?
  
• A circle has a center that falls on the line #y = 6/7x +7 # and passes through # ( 7 ,8 )# and #(3 ,9 )#. What is the equation of the circle?
  
• How do you find all points on the graph of #f(x)=sin^2x# at which the tangent line is horizontal?
  
• How do you integrate #int ln(2x+1)# by integration by parts method?
  
• What is the limit of #(e^t - 1) / t^3# as t approaches 0?
  
• What is the equation of the normal line of #f(x)=(1-x)e^(3x)-e^x# at #x=1#?
  
• An isosceles triangle has sides A, B, and C with sides B and C being equal in length. If side A goes from #(7 ,4 )# to #(2 ,1 )# and the triangle's area is #18 #, what are the possible coordinates of the triangle's third corner?
  
• Triangle A has an area of #18 # and two sides of lengths #9 # and #6 #. Triangle B is similar to triangle A and has a side of length #8 #. What are the maximum and minimum possible areas of triangle B?
  
• Question #084f4
  
• Question #084f4
  
• How do you minimize and maximize #f(x,y)=x/y-xy# constrained to #0<x-y<1#?
  
• What is the net area between #f(x) = 2/(x+1)^2 # and the x-axis over #x in [1, 2 ]#?
  
• Find b, c and d so that the quadrilateral is a parallelogram with area equal to 80 square units?
  
• How do you find the equation of a line tangent to the function #y=x^3+6# at (1,7)?
  
• Question #7dde7
  
• Anna is 6 ft. tall. She is walking away from a street light that is 24 ft tall at a rate of 4 ft/sec. How fast is the length of her shadow changing?
  
• Wha tis the sum of the first seven terms of the geometric series #3 + 12 + 48 + 192 + ...#?
  
• Question #60f1a
  
• How do you use Riemann sums to evaluate the area under the curve of #y = x^2 + 1# on the closed interval [0,1], with n=4 rectangles using midpoint?
  
• Question #2b61c
  
• How do you find the definite integral of #(x^4 - 1)/( x^2 + 1) dx# from -5 to -2?
  
• How do you integrate #int (x+1)^2ln3x# by integration by parts method?
  
• How can you easily visualize the size of the universe?
  
• How do you write a polynomial function given the real zeroes 2,-2,-6i and coefficient 1?
  
• How do you find the Limit of #ln(lnx) / x# as x approaches infinity?
  
• Question #297e2
  
• Find the polynomial #P(x)# with real coefficients such that #P(2)=12# and #P(x^2)=x^2(x^2+1)P(x)# for each #x in RR#?
  
• Given #tantheta=5/12# and #pi<theta<(3pi)/2#, how do you find #cos2theta#?
  
• A line segment is bisected by a line with the equation # 4 y + 3 x = 4 #. If one end of the line segment is at #( 8 , 1 )#, where is the other end?
  
• What is the equation of the normal line of #f(x)= -xln(4^(1-x))# at #x = 1#?
  
• How do you integrate by substitution #int 1/sqrt(2x)dx#?
  
• Given #f:[0,1]->RR# an integrable function such that #int_0^1f(x)dx=int_0^1 xf(x)dx= 1# prove that #int_0^1f(x)^2dx ge 4#?
  
• How do you find the limit of #(x-5)/(x^2-25)# as #x->5#?
  
• Question #29d47
  
• How do you find the equation of the line that is tangent to #f(x)=x^3# and parallel to the line #3x-y+1=0#?
  
• How do you use the epsilon delta definition to prove that the limit of #x^3+6x^2=32# as #x->2#?
  
• Question #ee0bc
  
• How do you solve #(1/9)^m=81^(m+4)#?
  
• How can you use trigonometric functions to simplify # 7 e^( ( 3 pi)/8 i ) # into a non-exponential complex number?
  
• How do you solve #cos^2x+6cosx+4=0# in the interval [0,360]?
  
• A triangle has corners at points A, B, and C. Side AB has a length of #24 #. The distance between the intersection of point A's angle bisector with side BC and point B is #4 #. If side AC has a length of #28 #, what is the length of side BC?
  
• How do you find the points where the graph of the function #y=tan(x)-x# has horizontal tangents?
  
• Two circles have the following equations #(x -8 )^2+(y -2 )^2= 36 # and #(x -1 )^2+(y +5 )^2= 81 #. Does one circle contain the other? If not, what is the greatest possible distance between a point on one circle and another point on the other?
  
• How do you simplify #(10k^2+55k+75)/(20k^2-10k-150)# and find any non permissible values?
  
• How do you convert #sqrt3 - i# to polar form?
  
• Question #ec66c
  
• How do you use the limit definition of the derivative to find the derivative of #f(x)=3x^2+3x+3#?
  
• How do you write 24/25 as a percent?
  
• How do you solve #(b+8)/23=-10#?