Answers edited by sente

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• Suppose that #lim_(xrarrc) f(x) = 0# and there exists a constant #K# such that #∣g(x)∣ ≤ K " for all " x nec# in some open interval containing c. Show that# lim_(x→c) (f(x)g(x)) = 0#?
  
• In 1/6=1.6666..., repeating 6 is called repeatend ( or reptend ) . I learn from https://en.wikipedia.org/wiki/Repeating_decimal, the reptend in the decimal form of 1/97 is a 96-digit string. Find fraction(s) having longer reptend string(s)?
  
• Does this word construction (a meditation on Exodus 3) count as poetry, and if so how would you classify it?
  
• What is the frequency of #f(theta)= sin 3 t - cos 21 t #?
  
• How do you solve 2015 AP Calculus AB Question #1?
  
• How do you differentiate #p(y) = y^2sin^2(y)cos(y)# using the product rule?
  
• In the triangle embedded in the square what is the measure of angle, #theta#?
  
• What is the distance between #(0, 0, 8) # and #(9, 2, 0) #?
  
• How do you convert #(3, -3sqrt3)# to polar form?
  
• The movement of a certain glacier can be modelled by d(t) = 0.01t^2 + 0.5t, where d is the distance in metres, that a stake on the glacier has moved, relative to a fixed position, t days after the first measurement was made. Question?
  
• How do you use DeMoivre's Theorem to find #(1+i)^20# in standard form?
  
• What is #(-7pi)/8 # radians in degrees?
  
• What is 0.09 (repeating) as a fraction?
  
• How do you integrate # 1/(1+e^x) # using partial fractions?
  
• How do you simplify #-2/(3-i)#?
  
• How do you graph #g(x)= log_6 x#?
  
• Question #de166
  
• Question #2b5bb
  
• Question #a71e9
  
• How do you simplify #(sina+tana)/(1+cosa)#?
  
• What are complex numbers?Thanx.
  
• Is #sqrt33# an irrational number?
  
• What is 1 divided by 0.2?
  
• How do you show that integration of #x^m e^(ax)dx = (x^m e^(ax) )/a - m/a int x^(m-1) e^(ax) dx#?
  
• Question #5d611
  
• How do you perform inversions for #y = x^2 and y = x^4?# Is #(dx)/(dy)# from the inverse #1/((dy)/(dx))?#
  
• Find the area of the shaded region (green) knowing the side of square is #s = 25 cm#?
  
• How to write the first four terms of the Maclaurin series for the function f(x)=(x+1)e^(2x) given that ?
  
• Question #b5ab2
  
• How do you simplify #((2n)!)/(n!)#?
  
• How do I find the natural log of a fraction?
  
• What are the all the solutions between 0 and 2π for #sin2x-1=0#?
  
• What is #1/3# of #18#?
  
• How do I graph the ellipse with the equation #x^2+4y^2-4x+8y-60=0#?
  
• Question #6d8e6
  
• How do you simplify # cos (pi - theta)#?
  
• Write the equation of a function with domain and range given, how to do that?
  
• Question #9e52a
  
• What is the product of #2x^2+7x-10# and #x+5# in standard form?
  
• Does #a_n=1/(n!) # converge?
  
• How do you show that if #a+b=0#, then the slope of #x/a+y/b+c=0# is #1#?
  
• How do you find all solutions to #x^5+243=0#?
  
• Among all pairs of numbers with a sum of 101, how do you find the pairs whose product is maximum?
  
• How do you find the number of terms in the following geometric sequence: -409.6, 102.4, -25.6,..., 0.025?
  
• The center of a circle is at (0,0) and its radius is 5. Does the point (5,-2) lie on the circle?
  
• How do you solve #sin^2 x - cos^2 x=0# for x in the interval [0,2pi)?
  
• 6 equal circular discs placed so that their centres lie on the circumference of a given circle with radius (r), and each disc touches its 2 neighbours. What is the radius of a 7th disc placed in the centre which will touch each of the each existing ones?
  
• Question #da791
  
• What's the LCM of 6 and 8?
  
• Is #sqrt(2)^(sqrt(2))# rational ? And #sqrt(2)^(sqrt(2)^sqrt(2))#?. And #sqrt(2)^(sqrt(2)^(sqrt(2)^cdots))#?
  
• How do you solve #2/(x+3)-4/(x^2+2x-3)=1/(1-x)#?
  
• How do you simplify # (x^(1/3) + x^(-1/3))^2#?
  
• How do you simplify # (2+2i)/(1+2i) # and write in a+bi form?
  
• If # n = 1/4#, what is the value of #(2n-5)/n#?
  
• If the zeros of #x^5+4x+2# are #omega_1#, #omega_2#,.., #omega_5#, then what is #int 1/(x^5+4x+2) dx# ?
  
• What is #lim_(x->0) (x^3+12x^2-5x)/(5x)# ?
  
• How do you express #sqrt(-4/5)# as a product of a real number and i?
  
• A composite geometrical shape is made up of a square, equilateral and right triangles. Calculate the area of hatched triangle?
  
• What is the value of #1/n sum_{k=1}^n e^{k/n}# ?
  
• How do you solve #120=100(1+(.032/12))^(12t)#?
  
• What is the derivative of #f(x) = (lnx)^(x)#?
  
• How do you solve #log x + log (x-3) = 1#?
  
• Question #98d02
  
• Question #a43bd
  
• Question #9c5a0
  
• Suppose there are m Martians & n Earthlings at a peace conference. To ensure the Martians stay peaceful at the conference, we must make sure that no two Martians sit together, such that between any two Martians there is at least one Earthling?(see detail)
  
• Question #e07a4
  
• Question #d2752
  
• Question #0f6bd
  
• Find the matrix #A# for the linear transformation #T# relative to the bases #B = {1,x,x^2}# and #B' = {1,x,x^2,x^3}# such that #T(vecx) = Avecx#?
  
• ?How do you find the sum of the infinite geometric series 0.03, 0.03, 0.003?
  
• Question #db818
  
• Is there a systematic way to determine the number of numbers between 10 and, say, 50, divisible by their units digits?
  
• How do you solve #tan^2 x=tan x#?
  
• How do you verify #(cosX+sinX)/(cscX+secX) = (cosX)(sinX)#?
  
• How do you find the number of terms in the following geometric series: 100 + 99 + 98.01 + ... + 36.97?
  
• Solve for #x in RR# the equation #sqrt(x+3-4sqrt(x-1))+sqrt(x+8-6sqrt(x-1))=1# ?
  
• How do you use the ratio test to test the convergence of the series #∑(2k)!/k^(2k) # from n=1 to infinity?
  
• How do you prove #sec^2 x - cot^2 ( pi/2-x) =1#?
  
• How do you solve #tan^-1(2x)+tan^-1(x)= (3pi)/17#?
  
• Determine the interval whereby 6x^2 + 44x + 70 ≥ 0?
  
• How do I perform matrix multiplication?
  
• Question #c5432
  
• What is #int_0^pi (lnx)^2 / x^(1/2)#?
  
• What is the Taylor series for #f(x)= cosx# centered on #x= pi/3#?
  
• A 45-45-90 triangle has a hypotenuse of length 14 units. What is the length of one of the legs?
  
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