Using Different Methods In Exercises 19-22, find
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Calculus (MindTap Course List)
- B- Find the directional derivative of the function W = x² + xy + z³ at the point P: (2,1,1) in the direction towards P₂(5,4,2). əz Ju əv B- If Z = 4e* Iny, x = In(u cosv) and y = u sinv find andarrow_forwardFind the directional derivative of the function at the given point in the direction of the vector v.. f(x,v) = e3xV – y?, (0,- 1), v= (2,3) -5 а. V5 7 b. V5 -7 C. d. -7 e V3arrow_forwardExercise 1: Show that the functions are orthogonal the indicated interval. a) f(x) = x, g(x)=x², x = [-2.2] c) f(x) = r, g(x) = cos 2r, x[-/2, π/2] b) f(x)=e¹, g(x) = re-e, r€ [0,2]arrow_forward
- Vector Calculus 1) Find the directional derivatives as a shown function of f at P (1,2,3) in the direction from P to Q (4,5,2) f(x, y, z) = x³y – yz² + zarrow_forwardQI: Consider the points A, B. C, D where coordinates are respectively (1,1,0). (-1,1,0). 0,-1,1). Find the direction cosines of AC and BD and calculate the angle between them. Q2: Let z = x?y, x = t2, y = t. Calculate by (a) the chain rule, (b) expressing z as a function ot f and finding 4 directly. Q3: Let z = 4x? – 8 x y* + 7y - 3. Find all the first and second order partial derivatives of z.arrow_forwardWrite the function f(z) = z + 1/z in the form f(z) = u(r, theta) + iv(r, theta) (Answer is f(z) = (r + 1/r)cos(theta) + i(r - 1/r)sin(theta)arrow_forward
- Exercise II (a) Determine the directional tangent lines to the given function at a given point. (i) f(r,y) = 3 cos(x) sin(y) in the direction of v = (1,2) at point (5, ). (ü) f(r, y) = 2? – 2x – y? + 4y in the direction of v = (1, 1) at point (1,2). (b) Determine the two points that are 2 units from the given surface at a given point. (i) f(r,y) = 3 cos(x) sin(y) in the direction of v = (1,2) at point (, ). (iü) f(r,y) = x² – 2x – y? + 4y in the direction of v = (1, 1) at point (1,2). %3Darrow_forwardAnother derivative combination Let F = (f. g, h) and let u be a differentiable scalar-valued function. a. Take the dot product of F and the del operator; then apply the result to u to show that (F•V )u = (3 a + h az (F-V)u + g + g du + h b. Evaluate (F - V)(ry²z³) at (1, 1, 1), where F = (1, 1, 1).arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning