Calculus Answers

Let 𝐹 = 2𝑥𝑧𝑖 − 𝑥𝑗 + 𝑦²𝑘. Evaluate 𝑉 𝐹𝑑𝑉 is the region bounded by the surfaces 𝑥 = 0, 𝑦 = 0, 𝑧 = 𝑥² , 𝑧 = 4.

Evaluate 𝐹 ∙ 𝑛𝑑𝑆, where 𝐹 = 4𝑥𝑧𝑖 − 𝑦 ² 𝑗 + 𝑦𝑧𝑘 and S is the surface of the bounded by 𝑥 = 0, 𝑥 = 1, 𝑦 = 0, 𝑦 = 1, 𝑧 = 0, 𝑧 = 1.

Find the total work done in moving a particle in a force field given by 𝐹 = 3𝑥𝑦𝑖 − 5𝑧𝑗 + 10𝑥𝑘 along the curve x = 𝑡 2 + 1, 𝑦 = 2𝑡2 , 𝑧 = 𝑡 3 𝑓𝑟𝑜𝑚 𝑡 = 1 𝑡𝑜 𝑡 = 2.

f(x)=tanx-1/secx

f(x)=cos√sin(tanπx)

The function is given : f(x) = (3+x)/4. Find f^-1(x).

Evaluate the iterated Integral  in terms of e. 

Find the limit of {n^3/(n^4+1)} as n →∞

Find fx(0,0) and fx(x,y), where (x,y) not = (0,0) for the function f:R^2 is to R defined by

F(x,y)={xy^3/x^2+y^2 if (x,y) is not= (0,0) and (x,y)=(0,0).

Is Fx continuous at (0,0)? Justify your answer.

Find the derivative of f(v)=3 sqrt v-2ve/v