Calculus Questions Set 6:
What does k = limx→1 (1-x2)1/log(1-x) evaluate to?
Solution:
Find lim(x,y)→(0,0) y^6 / (x^10 * y^2 + x^15)
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What is the value of the integral ∫0π sin6x cos4x dx?
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Evaluate the integral using Laplace transformation:
∫0∞ sin(mt)/t dt
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If Q(x, y) is the mid - point of line segment joining A(-1,3) and B(7,5) then the value of x + y is
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Points C and D trisect the line segment joining points A(4, 5) and B(16, 14). What is the length of the line segment CD?
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What is the slope of a line that makes an intercept of 5 in the positive direction of y axis and 1 in the negative direction of x axis?
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The area of the triangle whose vertices are given by the coordinates (1, 2), (-4, -3) and (4, 1) is :
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Which of the following statements is false?
Solution:
Let f and g be non-increasing and non-decreasing functions respectively from [0, ∞) to [0, ∞) and h(x) = f(g(x)), h(0) = 0, then find the condition for h(x) - h(1) in [0, ∞)
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