Questions asked by kamil9234

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• Prove this: #(1-sin^4x-cos^4x)/(1-sin^6x-cos^6x)=2/3#?
  
• Prove it: #sqrt((1-cosx)/(1+cosx))+sqrt((1+cosx)/(1-cosx))=2/abs(sinx)#?
  
• Prove it: #tan^5x=((1/(1-sinx)^2)-(1/(1+sinx)^2))/((1/(1-cosx)^2)-(1/(1+cosx)^2)#?
  
• Simplify the expression?: #1/(sqrt(144)+sqrt(145))+1/(sqrt(145)+sqrt(146))+...+1/(sqrt(168)+sqrt(169))#
  
• Solve this: #abs(2cos3x)=1# ---> (x=... + ...)?
  
• Solve this: #2sin2x+2sinx=2cosx+1#?
  
• Can someone give me a clue, how can i solve this? I want something like: #x=pi/4+kpi# ---> Solve this: #2sin^2(x)-sin^2(2x)=cos^2(2x)#
  
• Simplify the expression? #cos(270+2alpha)+sin(450+2alpha)#
  
• How many common points have #f# and #g# function graphs in the interval #<0;2pi># ?
  
• Simplify the expression:? #(sin^2(pi/2+alpha)-cos^2(alpha-pi/2))/(tg^2(pi/2+alpha)-ctg^2(alpha-pi/2))#
  
• If #tg^2alpha=3# then #sin^2(2alpha)# equal ...?
  
• **Determine all the values of the parameter m for which the operation: ** #4x^2-6mx+(2m+3)(m-3)# has TWO different real solutions. #x_1<x_2# #(4x_1-4x_2-1)(4x_1-4x_2+1)<0# ?
  
• PROVE THAT: Data: #a,b,c,x,y,z > 0# #1/x+1/y+1/z=1#?
  
• Prove that function hasn't lim in #x_0=0# ?
  
• Which of the following fractions has the decimal expansion completed?
  
• Find #lim_(x rarr oo) sqrt(x)/root3x# ?
  
• #f(x)=sqrt(x^4-1)+sqrt(1-x^8)# Which is set of function values? A) <0,1> B) {0} C) (0;infinite) D) (0;1>
  
• How many subsets does a set #{{{O/}}}# have?
  
• What is last digit #762^1816# ?
  
• How to calculate derivative? #(7x-1)^3(2x+1)^2#
  
• Ex with lim: #lim_(x->4) ((sqrt(2x-7)-1)/(sqrt(x-3)-1))# ?
  
• Which one is the smallest number? a) #0.02^(0.03)# b) #0.03^(0.02)# c) #log_(0.98) 1.01# d) #sin(0.02)# How to choose right answer quick?
  
• Prove that: (is true for any positive x,y):? #x^x*y^y>=((x+y)/2)^(x+y)#
  
• What is #P(AuuBuuC)#?
  
• Prove that? : #P(AuuBuuC)=P(A)+P(B)+P(C)-P(AnnB)-P(BnnC)-P(AnnC)+P(AnnBnnC)#
  
• Are disjoint events always independent?
  
• How many 8-character passwords can be created from 26 lowercase letters and 10 digits, assuming that in every password there must be as many letters and numbers as?
  
• In which of these situations the work done by the force acting on the slab will be greater?