wy ad let (s, 1-45 24. Suppose you have a function f(x, y) and a curve r(t). You know: Vf(x, y) = (y² cos(xy), ez+v), r' (t) = (5t + 7, (t + 2)² - 1), r(0) = (0, 2). Compute(for) 25. Find the gla It=0

Q: A particle moves along the curve *= 21² , y = t² – 4t and = = 31 – 5 where t is the time . Find the…

A: Given: Position vector is given as, r→=2t2i^+(t2-4t)j^+(3t-5)k^ The objective is to find the…

Q: Find the length of the curve described by y = V sec* t – 1 dt, - sI 4 4 (a) 4 (b) (c) (d) 2/2 (e) 1

A:

Q: 18 The equation 10 14 - 2 = 0 defines z as a function of x and y. Find dz/dx and dzldy at the point…

A: 18x+10y+14z-2=0∂∂x18x+10y+14z-2=∂∂x(0) [Differentiate both sides with respect to…

Q: 3. Given F(x,y)=(y,2x), find F-T ds where curve C is the parabola y=x from point (0,0) to point…

A: We use line integration to evaluate this.

Q: The slope of the curve y =x' + 3x² – 4x+5 at (1,5) is O a. 0 O b. 2 O c. 5 O d. 4

A:

Q: The equation of the tangent line to the curve x² + y? = 9, at (7,-18) is 7 y = 18 7 (х — 7) — 18 18…

A:

Q: Find an equation of the tangent plane at the given point. f (x, y) = x/√y,  (4, 4)

A: Given : The function is f ( x, y) = xy and point ( 4, 4 ).

Q: 7. By definition find the slope of curve y = x2 – 2x – 3, at P(2, 3).

A:

Q: me please: Suppose X1, X2 ∼ Unif(0, 1) and are independent. Let

A: We have given that X1, X2 ∼ Unif(0, 1)

Q: Q4) r(x, y) = xs -x/ay2 Does the function is harmonic

A: We know that a function in two variable is called harmonic if it satisfies the Laplace equation…

Q: 1.Solve the following polynomial equations.  a)  2X3+1=x2+2X

A:

Q: Determine the intersection point of the lines tangent to the curve r (t) = (senπt, 2senπt, cosπt) at…

A: The given curve is rt=sinπt,2sinπt,cosπt. Differentiating it with respect to t:…

Q: Find the equation of the tangent plane to the graph of the curve f(x, y) = x² + y² at the point…

A:

Q: Find an equation of the tangent plane to the graph y = x² + 2xz at (1,3, 1). (Possible Answer: 4r –…

A: We have to find an equation of the tangent plane to the graph y=x2+2xz at 1,3,1.

Q: (5) Find the curve y = f(x) in the xy-plane that passes through the point (9, 4) and whose slope at…

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Q: For the curve x (t) = t², y (t) =t³ – 3t Given the curve crosses itself at (3, 0), a) Find the…

A:

Q: uppose that x + y = 2. What is y" at the point (1, 1)?

A: