Answers edited by Cesareo R.

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• How do you find the Limit of #sqrt (x -1) / (sqrt(x+3) - 2) # as x approaches 1?
  
• What is the interval of convergence of #sum_1^oo [(3x)^n(x-2)^n]/(nx) #?
  
• How do you insert parentheses so the statement #4+10+8-9•8= -50# is true?
  
• In the diagram below, the small circle is centered at E, the large one is centered at O. The segments FC and OD have lengths as of 2.38 and 3 cm respectively. Find the length of CD and calculate shaded area?
  
• How do you solve # |x+2| + |2x-4| = |x-3| #?
  
• What is a solution to the differential equation #dy/dx=2yx+yx^2#?
  
• How do you find all the critical points to graph #9x^2 – y^2 – 36x + 4y + 23 = 0 # including vertices, foci and asymptotes?
  
• Question #5e9cc
  
• How do you use a linear approximation or differentials to estimate #(2.001)^5#?
  
• How do you prove that AB = BA if and only if AB is also symmetric?
  
• How to find the distance from the point A(3,-5,5) to the line x = 2 + 3t , y= 1-2t, z= -1 + t ?
  
• How do you minimize and maximize #f(x,y)=x+y# constrained to #0<x+3y<2#?
  
• The Functional Continued Fraction (F C F) of exponential class is defined by #a_(cf) (x;b) = a^(x+b/(a^(x+b/a^(x +...)))), a > 0#. Upon setting a = e = 2.718281828.., how do you prove that #e_(cf) ( 0.1; 1 ) = 1.880789470#, nearly?
  
• What is the interval of convergence of #sum ((x − 4)^n)/(n*(−9)^n)#?
  
• How can I find the missing length of this triangular prism that's inside a sphere?
  
• How do you graph #y² - x² - 2y + 4x - 4 =0#?
  
• How do you integrate # (x^3)ln(x)dx#?
  
• How do you evaluate #log_49 7#?
  
• How do you minimize and maximize #f(x,y)=(e^(yx)-e^(-yx))/(2yx)# constrained to #1<x^2/y+y^2/x<3#?
  
• How do you find the limit of #[(1/ln(x+1)) - (1/x)]# as x approaches 0?
  
• How do you evaluate #int (x*arctanx) dx / (1 + x^2)^2# from 0 to infinity?
  
• How do you verify #sin^5xcos^2x=(cos^2x-2cos^4x+cos^6x)sinx#?
  
• Question #3057c
  
• Payton colored a composite shape made up semicircles whose diameters are the sides of a square. The result is a shape given below. Find the area of the shaded region (Petals) in terms of x? Calculate the area using the dimension in 2nd figure?
  
• How do you prove that the 4-sd approximation to the value of #log_2(2+1/log_2(2+1/log_2(2+...)))# is 1.428?
  
• How do you find #(d^2y)/(dx^2)# given #y+siny=x#?
  
• How do you find the parametric equations for the rectangular equation #x^2+y^2=16#?
  
• How do you find the limit of #(ln x^2) / (x^2-1)# as x approaches 1?
  
• How do you find the limit of # ln ( 3x + 5e^x )/ ln ( 7x + 3e^{2x})# as x approaches infinity?
  
• If #alpha, beta# are the roots of #x^2+px+q=0# and also of #x^(2n) + p^nx^n + q^n# = 0 and if #alpha/beta, beta/alpha# are the roots of #x^n + 1 + (x+1)^n = 0 ,# then prove that n must be an even integer?
  
• Is #3[g(x)]= x# a linear function?
  
• Question #764bc
  
• What is the interval of convergence of #sum_{k=0}^oo 2^(k) / ((2k)!* x^(k)) #?
  
• What is #int_0^pi (lnx)^2#?
  
• How do you find the Limit of #(sin^3 x )/ (sin x - tan x)# as x approaches 0?
  
• From a unit sphere, the part between two parallel planes equidistant from the center, and with spacing 1 unit in-between, is removed. The remaining parts are joined together face-to-face, precisely. How do you find the volume of this new solid?
  
• With what exponent the power of any number becomes 0? Like we know that (any number)^0=1,so what will be the value of x in (any number)^x=0?
  
• A fence 4 feet tall runs parallel to a tall building at a distance of 2 feet from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building?
  
• How do you find the value of a given the points (-9,7), (a,5) with a distance of #sqrt29#?
  
• Question #58880
  
• How do you integrate #int e^-x/(9e^(-2x)+1)^(3/2)# by trigonometric substitution?
  
• What is the indefinite integral of #sin (lnx) dx#?
  
• How do you prove #log_(b^n)(x^n)=log_(b)x#?
  
• How do you find the limit of # [sqrt (h^2 + 4h + 5) - sqrt(5)] / h # as h approaches 0?
  
• Advanced Quadratic drag - How to solve?
  
• How do you integrate #int x^2e^-x# by integration by parts method?
  
• Find the number of four tuples (a,b,c,d) of positive integers satisfying all three equations #a^3=b^2#, #c^3=d^2#, #c-a=64# ?
  
• A ball with a mass of #450 g# is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of #12 (kg)/s^2# and was compressed by #4/5 m# when the ball was released. How high will the ball go?
  
• How do you find all the real and complex roots of #F(x)=x^5-1#?
  
• How do you solve the system #4x^2-56x+9y^2+160=0# and #4x^2+y^2-64=0#?
  
• How do you solve #x^4-10x^3+27x^2-2x-40>=0#?
  
• How do you minimize and maximize #f(x,y)=(2x-y)+(x-2y)/x^2# constrained to #1<yx^2+xy^2<3#?
  
• How do you find the vertical, horizontal or slant asymptotes for #f(x)=(2x)/sqrt (9x^2-4)#?
  
• How do you express #f(theta)=2cos^2(2 theta) + sin^2(4theta)-5tan^4theta# in terms of non-exponential trigonometric functions?
  
• How do you integrate #sin( ln x )#?
  
• How do you find the inverse of #f(x)=ln(2+ln(x))#?
  
• How do you evaluate the continued fraction #f(e)=e-1+1/(e-1+1/(e-1+1/(e-1+1/(e-1+1/...# ?
  
• Factorize #2 x^2 + y^2 + 3 x y + 6 x - 15 = 0# ?
  
• What is the graph of the Cartesian equation #(x^2 + y^2 - 2ax)^2 = b^2(x^2 + y^2)#?
  
• What is #sin^6theta# in terms of non-exponential trigonometric functions?
  
• How do you graph the inequality #2x - 3y>9# and #- x - 4y> 8#?
  
• How do you find a power series representation for # f(x)=(x / (x^(2)-3x+2) )# and what is the radius of convergence?
  
• What is the interval of convergence of #sum (2+2/n)^n((x-1)/2)^n#?
  
• If #x^2 + y^2 = 73 # and #xy =24#, what is the value of #(x+y)^2# ?
  
• How do you write an equation of a circle whose center is at P(4,-5) and is tangent to the line -x+2y=1?
  
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