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Lamar U 2nd way: evaluate exp integral ∫e^(2x)/(1+e^(2x)) dx
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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx
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AI 2008 Hindustan: Evaluate integral ∫ 2/3 cos(x)/sin^2(x) dx
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lim x/e^x? as x→∞
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exp Differentiate (i) b^e^x (ii) b^x&e (iii) (b^e)^x (iv) (b^x)^e
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partial Let f(x,y,z)=x e^(yz). Compute fxzy & fyxz.
2nd way: integral ∫(6+4x--2x^2) dx via 1) complete sq 2) then trig. sub
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Find the 2nd-order partial derivatives of f(x,y)=2xy^2-3x^2+xy^3
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prob stat: 2 ways Joe's mean mark for the physics tests for the term was 72.
AP Calculus: integral ∫ln(a+bx^2) dx
1)integral ∫ x dx 2)integral ∫ ln(x)/x dx via inspection [NO u-sub]
Sum of the first n integers 1+2+3+ ...+n=n/2 (1+n) via Induction
Lamar U 2nd way: evaluate exp integral ∫e^(8x)(4+e^(4x))^(-3) dx
2 ways: trig integral cos^2(x) sin^2(x) dx
NYU: 2 ways compute log integral ∫ln(x) dx
Let B be the mx1 col. matrix [1/m ... 1/m]'. If A =[a1 ... am] is any row matrix. What is AB?
Evaluate these 7 integrals ...
Purdue U: trig integral ∫tan^3(x) sec^2(x) dx =? where x=0 to pi/4
Suppose z is differentiable funtion of x & y that is defined implicitly x^2+y^3-z+2yz^2=5
U Penn: Assuming g(x) is a continuous function whose derivative g'(x) is also continuous, evaluate .