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The function y = ex is one of the special functions of analysis and can be defined as the sum of an ___________ series
assume all curves joining a given point (0,3) to a point on the x-axis, such that it encloses an area=12 together with the x-axis (i.e. area under the curve and above the x-axis is 12). find equation of the curve which generates the least area when rotated about the x-axis.
Let 𝑭 = 𝒙𝒛𝒊 − 𝒙𝒋 + 𝒚 𝟐𝒌. Evaluate ∭ 𝑭𝒅𝑽 𝑽 where V is the region bounded by the surfaces 𝒙 = 𝟎, 𝒚 = 𝟎, 𝒚 = 𝟏, 𝒛 = 𝒙 𝟐 , 𝒛 = 𝟏
If 𝑭 = 𝟔𝒙𝒛𝒊 − 𝟐𝒚 𝟐 𝒋 + 𝒚𝒛𝒌, evaluate ∬ 𝑭 ∙ 𝒏𝒅𝑺 𝑺 where S is the surface of the cube bounded by 𝒙 = 𝟎, 𝒙 = 𝟏, 𝒚 = 𝟎, 𝒚 = 𝟏, 𝒛 = 𝟎, 𝒛 = 𝟏
If ∅ = 𝟐𝒙𝒚𝒛 𝟐 , 𝑭 = 𝒙𝒚𝒊 − 𝒚𝒋 + 𝒙 𝟐𝒌 𝐚𝐧𝐝 𝑪 𝐢𝐬 𝐭𝐡𝐞 𝐜𝐮𝐫𝐯𝐞 𝒙 = 𝒕 𝟐 , 𝒚 = 𝟐𝒕, 𝒛 = 𝒕 𝟑 𝐟𝐫𝐨𝐦 𝒕 = 𝟎 𝒕𝒐 𝒕 = 𝟏, 𝐞𝐯𝐚𝐥𝐮𝐚𝐭𝐞 𝐭𝐡𝐞 𝐥𝐢𝐧𝐞 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐥𝐬 a. ∫ ∅𝒅𝒓 𝑪 , b. ∫ 𝑭 𝑿 𝒅𝒓.
If 𝑭 = 𝟑𝒙𝒚𝒊 − 𝒚 𝟐 𝒋 evaluate ∫ 𝑭 ∙ 𝒅𝒓 where C is the curve in the xy plane, 𝒚 = 𝟐𝒙 𝟐 , from (0,0) to (1,2)
Find the area between two curves: y^2 = 2x + 3 ; y = x
If the terms of a sequence are considered as a sum, for instance,1+x+x2 + ---, the expression is called a ______________
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If the terms of a sequence are considered as a sum, for instance,1+x+x2 + ---, the expression is called a ______________
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F(x)=x^3-x^2-8x+12
Write the values of x for which f'(x)>0
