Answers edited by Cesareo R.

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• What is the interval of convergence of #sum_1^oo (2^k)/k (x-1)^k #?
  
• How do you find the vertical, horizontal or slant asymptotes for #y=(2x^2-3x+4)/(x+2)#?
  
• Question #71203
  
• How will you prove the formula #sin(A-B)=sinAcosB-cosAsinB# using formula of scalar product of two vectors?
  
• How do you express #1/ (x^4 +1)# in partial fractions?
  
• How do you identify the following equation #(x - 1)^2 + y^2/25 = 1# as a circle, parabola, ellipse or hyperbola?
  
• What are the asymptotes for #(x^2 - 2x - 3 )/(-4x) #?
  
• How do you convert #r=6sin(theta)# to rectangular form?
  
• How do i determine the distance between #x^2+y^2-z^2=1# and the point #P(1,3,1)# ?
  
• What is the equation of the line normal to # f(x)=lnx-x# at # x=2#?
  
• How do you solve #log_(1/3) (x^2 + 4x) - log_(1/3) (x^3 - x) = -1#?
  
• #i ^i = # ?
  
• Question #120b5
  
• How do you implicitly differentiate #2(x^2+y^2)/x = 3(x^2-y^2)/y#?
  
• How do you solve #sqrt(20-X) + 8= sqrt( 9-X) +11#?
  
• A parallelogram has sides with lengths of #14 # and #8 #. If the parallelogram's area is #84 #, what is the length of its longest diagonal?
  
• #P(x)# is a polynomial function. If #P(x^2) = (a-b+2)x^3 - 2x^2 + (2a+b+7)x - 20# , what is #P(a+b)# ?
  
• Find the maximum possible total surface area of a cylinder inscribed in a hemisphere of radius 1?
  
• If#""f^2(x)+g^2(x)+h^2(x)<=9# and #u_x=3f(x)+4g(x)+10h(x)#, again #(u_x)_"max"=sqrtn,"where"" "ninN# then what is the value of n?
  
• How do you solve # |x+2| + |2x-4| = |x-3| #?
  
• How do you find all the real and complex roots of #x^3+x^2+x+2#?
  
• A superball that rebounds 3/10 of the height from which it fell on each bounce is dropped from 38 meters. ?
  
• How do you find the radius of the circle #x^2 + y^2 - 4x + 6y - 12 = 0#?
  
• If#" "veca=3hati+4hatj+5hatk and vec b= 2hati+hatj-4hatk# ;How will you find out the component of #" "veca " ""perpendicular to" " " vecb#?
  
• The perimeter of a triangle is 60 cm. it's height is 17.3. what is its area?
  
• How do you simplify # [(3+2i)^ 3 / (-2+3i)^4] #?
  
• How do you implicitly differentiate #11=(x)/(1-ye^x)#?
  
• How do you find the limit of #( e^(3t) - 1 ) / t# as x approaches 0?
  
• How do you minimize and maximize #f(x,y)=xe^x-y# constrained to #0<x-y<1#?
  
• Determine the sum of the series 1, 1/2, 1/4, 1/8 .......... t(14)?
  
• A circle has a center that falls on the line #y = 3/7x +1 # and passes through # ( 2 ,1 )# and #(3 ,5 )#. What is the equation of the circle?
  
• Calculate #sum_{n=0}^{infty}n^3((x+1)/2)^n# ?
  
• Question #63619
  
• How do you minimize and maximize #f(x,y)=x^2+y^3# constrained to #0<x+3xy<4#?
  
• Using the integral test, how do you show whether #sum 1 / [sqrt(n) * (sqrt(n) + 1)]# diverges or converges from n=1 to infinity?
  
• Does #sum_{n=2} 1 / (1 + n ( Ln(n) )^2)# converges or diverges from n=2 to infinity?
  
• What is a solution to the differential equation #(x+1)y'-2(x^2+x)y=e^(x^2)/(x+1)# where x>-1 and y(0)=5?
  
• Is #f(x)=-x^5-21x^4-2x^3+4x-30# concave or convex at #x=0#?
  
• How do you find the linearization at (2,9) of #f(x,y) = xsqrty#?
  
• How do you find vertical, horizontal and oblique asymptotes for #x^3/(x^2-4)#?
  
• If the roots of the equation #ax^2+2bx+c=0# are real and distinct then find the nature of the roots of the equation #(a+c)(ax^2+2bx+c) = 2(ac - b^2)(x^2+1)#?
  
• How do you find the volume of the solid formed by rotating the region enclosed by ?
  
• How do you divide #(x ^ 10 + x ^ 8) / (x - 1)#?
  
• Solve the following system of equations: #(x^2+y^2=29),(xy=-10)# ?
  
• How do you integrate #int 1/(x^2+x+1)# using partial fractions?
  
• How do you find the linear approximation L to f at the designated point P. compare the error in approximating f by L at the specified point Q with the distance between P and Q given #f(x,y) = 1/sqrt(x^2+y^2)#, P(4,3) and Q(3.92, 3.01)?
  
• Circle in polar coordinates ?
  
• A triangle has sides with lengths of 6, 4, and 3. What is the radius of the triangles inscribed circle?
  
• How do I find the points on the ellipse #4x^2 + y^2 = 4# that are furthest from #(1, 0)#?
  
• How do you find a unit vector u in the same direction as the vector ⟨1,−2,−3⟩?
  
• How do you find a power series representation for #(x-2)^n/(n^2) # and what is the radius of convergence?
  
• How do you solve #2^(x) - 2^(-x) = 5#?
  
• The recursive sequence is defined by the formula #t_n=2t_(n-1)+3#; and #t_1=-2#, how do you find #t_6#?
  
• What is the equation for the line of symmetry for the graph of the function #y=-4x^2+6x-8#?
  
• How do you find the measure of each exterior angle of a regular 11-gon?
  
• How do you minimize and maximize #f(x,y)=(x-2)^2/9+(y-3)^2/36# constrained to #0<x-y^2<5#?
  
• How do you minimize and maximize #f(x,y)=x^2y-xy# constrained to #3<x+y<5#?
  
• Solve for equilibrium ?
  
• How can you use a truth table to prove that #((~p vv q) ^^ p) vv q# is equivalent to #q# ?
  
• How do you solve #(x-1)^[log(x-1)]=100(x-1)#?
  
• Two forces #vecF_1=hati+5hatj and vecF_2=3hati-2hatj# act at points with two position vectors respectively # hati and -3hati +14hatj# How will you find out the position vector of the point at which the forces meet?
  
• Do #f(x) = 6 – 10x^2# and #g(x) = 8 – (x – 2)^2 # share any tangent lines?
  
• For what r does #3/(n^(2r - 3))-3/n# converge or diverge?
  
• Advanced Quadratic drag - How to solve?
  
• What is the sum of the exterior angle measures for an irregular convex octagon?
  
• How do you find the volume of a solid where #x^2+y^2+z^2=9# is bounded in between the two planes #z+2x=2# and #z+2x=3#?
  
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