Applied Calculus for the Managerial Life and Social Sciences Exam Test 2025/2026 Graded A+

Applied Calculus for the Managerial Life and Social
Sciences Exam Test 2025/2026 Graded A+


fu⃗(a,b)=||∇f(a,b)|| - ANSWER -FALSE


Suppose fx(a,b) and fy(a,b) both exist. Then there is always a direction
in which the rate of change of f at (a,b) is zero. - ANSWER -TRUE


The gradient vector ∇f(a,b) is tangent to the contour of f at (a,b). -
ANSWER -FALSE


If u is perpendicular to ∇f(a,b) then fu(a,b) = <0,0> - ANSWER -FALSE


fu(a,b) is parallel to u. - ANSWER -FALSE


If u is a unit vector, then fu(a,b) is a vector. - ANSWER -FALSE


If f(x,y) has fx(a,b) = 0 and fy(a,b) = 0 at the point (a,b) then f is constant
everywhere. - ANSWER -FALSE


∇f(a,b) is a vector in 3D space. - ANSWER -FALSE


∫ xⁿ dx

pg. 1

, Power Rule - ANSWER -[xⁿ⁺¹]/(n+1) + C


∫ k*f(x) dx
Multiplication by constant - ANSWER -k*∫ f(x) dx


∫ [f(x)+g(x)] dx
Sum Rule - ANSWER -∫ f(x) dx + ∫ g(x) dx


∫ [f(x)-g(x)] dx
Difference Rule - ANSWER -∫ f(x) dx - ∫ g(x) dx


∫ (1/x) dx - ANSWER -ln|x| + C


∫ eˣdx - ANSWER -eˣ + C


∫ aˣ dx - ANSWER -aˣ/ln(a) + C


∫ ln(x) dx - ANSWER -xln(x) - x + C


Antiderivative - ANSWER -the function f (x) whose derivative is f '(x)




pg. 2