Using Different Methods In Exercises 7-12, find dw/dt (a) by using the appropriate Chain Rule and (b) by converting w to a function of t before differentiating.
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Chapter 13 Solutions
Student Solutions Manual For Larson/edwards? Multivariable Calculus, 11th
- Let f(x, y, z) = x*y+ + z* and r = st, y = st, and z = (a) Calculate the primary derivatives af (b) Calculate as ds (C) Use the Chain Rule to compute af ds In (C) express your answer in terms of the independent variables t, s || || ||arrow_forward(MULTIPLE CHOICE) Determine which of the following set of functions is(are) linearly depen- dent on (-0o, 0). (A) fi(x) = x, f2(x) = x², f3(x) = 4x – 3x? (B) fi(x) = 5, f2(x) = cos? r, f3(x) = sin? r %3D %3D (C) fi(x) = x, f2(x) = x - 1, f3(x) = x +3 (D) fi(x) = e, f2(x) = e2", f3(x) = e- (E) fi(x) = e, f2(x) = e, f3(x) = sinh a %3Darrow_forwardcomplete solution fourier transform:arrow_forward
- 2x+1 The gradient vector to f (x, y) at the point (0, 0) y+1 is .arrow_forwardCalculusarrow_forwardEXAMPLE 4 Write out the Chain Rule for the case where w = f(x, y, z, t) and x = x(u, v), y = y(u, v), z = z(u, v), and t = t(u, v). SOLUTION We apply theorem 4 with n = and m = 2. The figure shows the tree diagram. Although we haven't written the derivatives on the branches, it's understood that if a branch leads from y to u, then the partial derivative for the branch is ây/ðu. With the aid of a tree diagram, we can now write the required expressions: aw ax дх ди aw ay ду ди aw dz + aw at at du aw Video Example ) + + du az du aw dy + aw at aw dz + az əv at av dw дw дх %3D dv дх ду dy avarrow_forward
- = Either f,g,h € F(R, R) the functions f(x) sin(x)^2 And g(x) = cos(x) and h(x) = sin(x). Show that f, g and h are linearly independent =arrow_forwardx*y+2x? Let f(x, y) = and find f,(1,2) and f,(1,2) 3x- yarrow_forwardFourier transform of f(t) = 3te²tu(t) is Select one: 3 iw-2 2 (iw)2–22 3 (iw-2)2 3 iw+2 iw iw²–2²arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning