Questions asked by 808math

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• What is the limit of #((1)/(x))-((1)/(e^(x)-1))# as x approaches infinity?
  
• What is the limit of (1+(a/x) as x approaches infinity?
  
• What is the limit of ((1/x)-((1)/(e^(x)-1)) as x approaches 0^+?
  
• What is #lim_(xto0^+) ((1/x)-((1)/(e^(x)-1)))#?
  
• What is the limit of (1+(4/x))^x as x approaches infinity?
  
• What is the #lim_(xrarr1^+) x^(1/(1-x))# as x approaches 1 from the right side?
  
• Differentiate y=lnsinx-(1/2)sin^(2)x ?
  
• Differentiate y=ln(cosh 3x)?
  
• How do you evaluate the integral? #int_0^(pi/2)cos^(3)x sin2x dx#
  
• How do you evaluate this integral? #int_-3^3 x/(1+|x|)dx#
  
• Evaluate this integral?
  
• How do you evaluate this integral?
  
• How do you evaluate the integral?
  
• How do evaluate the integral below?
  
• How do you find the area of the region bounded by the given curves?
  
• How do you find the volume of the solid obtained by rotating the region bounded by the curves about the y-axis?
  
• How do you find the volume of the solid obtained by rotating the region bounded by the curves about the x-axis?
  
• What is the momentum of these two sea creatures just after their collision?
  
• What is the area of the figure?
  
• How fast, and in which direction, must the person run to catch the ball at the level from which it was thrown?
  
• If a baseball player can throw a ball at 45° to a point 100m away horizontally to the initial vertical level, how high could he throw it vertically upward?
  
• What is the landing location of the projectile and its speed of impact?
  
• What is the landing point?
  
• The electron in a hydrogen atom orbits a stationary proton at a distance of 5.3*10^-11 m at a speed of 2.2*10^6 m/s. What is (a) the period (b) the force on the electron?
  
• What is the tension in the rope? And the horizontal and vertical forces exerted by the pivot?
  
• How do you Evaluate the integral by changing to cylindrical coordinates?