In each part, show that
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- Fill in the following blanks: If W = f(x, y, z) is a differentiable and x,y and z are differentiable functions of (t). dW ) can be written by dt By using Chain Rule, the formula of ( Two vectors are considered equivalent (equal) vectors if they The curvature of a plane or a space curve can be defined as If F(x, y) is a differentiable function and the equation F(x, y) = 0 defines (y) as a and dy ) can be written by dx function of (x). The formula ( The TNB frame plays an important role in If u and v are non-zero vectors, the cross product ( ux v ) can be calculated by two formulas which are andarrow_forwardLet x, y, z be vectors. Let f : R^2 → R be a function. Letr(t) be a vector-valued function. Determine if each of the following is a scalar, vector, or nonsense. No explanation is needed.a. x · yb. (x · y) × zc. [(x · y)z] × yd. r′(t)e. Duf(x, y)f. ∇xarrow_forwardwhen we calculate the directional derivatives of the function f(x,y,z)= x2+y3+z3 at the point (1,1,1) in different directions, which of the following values can obtiain? a ) -6 b) -4 c ) 1 d ) 5 e) 7arrow_forward
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- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage