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Calculus
Evulate ∫ (2x^2 + 3y^2)sc, where C is the curve
C
x(t)= at^2, y(t) = 2at, 0≤t≤1
C
x(t)= at^2, y(t) = 2at, 0≤t≤1
Calculus
Evaluate integral integral integral yz dv where E is the region bounded by x = 2y^2 + 2z^2 - 5 and the plane x = 1
Calculus
Does the function f(x,y)= (x^2-y^2)/(x^2+y^2), x
Calculus
State, with explanation, whether the following statements are True or False: a) If a real-valued function is defined on (−∞, 𝑐) ∪ (𝑐, ∞) and has a removable discontinuity at 𝑥 = 𝑐, then lim𝑥→𝑐 𝑓(𝑥) does not exist. b) Since 𝑓(𝑥) = 1 𝑥−1 + 1 has a vertical asymptote at 𝑥 = 1, the Intermediate Value Theorem cannot be used to find an existence of a root in the open interval (−1, 1 2 ).
Calculus
Let L be the line with equation y=x-1. Find the minimum distance between L and the point (4,5) by using (a) theorem 10.2.4, (b) the Method of Lagrange.
Calculus
Prove that
∑_(i=5)^20▒〖3.2^i 〗= ∑_(k=0)^15▒〖96.2^k 〗
Calculus
1.consider the r^2-r function f defined by f(x,y)=x^2-6x+3y^2-y^3. (a) find all the critical points of f. (the function has two critical points). (b) use theorem 10.2.9 to determine the local extreme values and minimax values of f. also determine (by inspection) whether any of the local extrema are global extrema
Calculus
Evaluate integration integration X(y-1) dA where R is the region bounded by y=1-x^2 and y=x^2-3
Calculus
Evaluate integration integration y^2+3x dA where R is the region in the 3rd quadrant between x^2 +y^2=1 and x^2+y^2= 3
Calculus
Evaluate integration integration y^2+3x dA where R is the region in the third quadrant between x^2+y^2=1 and x^2+y^2=3
