If r=xi-yj+zk and r= r|, prove that for differentiable function f(r) d'f 2 df show that vifr) = dr and hence find f(r) such that V?f(r)=0. r dr

Q: f(x,y,z) be a differentiable function the point P(2,5,-1). Let at Which of the following is the…

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Q: Determine the x-coordinate of the point for which the tangent is horizo Function f(x)-¹. X A) 3 B)…

A: Determine the x- coordinate of the point for which the tangent is horizontal to the function

Q: Suppose f is a differentiable function such that f(-2) = 3 and f(5) = 17. Then there must be a point…

A: Consider the conditions for the mean value theorem.

Q: Q2] Find the analytic function F(z) if u = coshy.cosx, (B.C. v-0 at x=0)

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Q: Define a function f : R² → R² by f 2.у 1. Show that f is differentiable on A = E R² |x > 0, y > 0}…

A: To show that the function f defined as below is differentiable on A and compute its derivative

Q: Let z be a differentiable function of x and y related by the equation: x z ++* =(√√y+cosh(z))". X 2…

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Q: Is there a twice differentiable function f R2R whose best adratic approximation at the point (1,0)…

A: Given problem is from differential calculus in several variables. We have shown that there exists a…

Q: 3. From results obtained in Secs. 21 and 23, determine where f'(z) exists and find its value when…

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Q: Check that the equation x³ + y³ + z³ = x + y + z implicitly defines at least one differentiable…

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Q: d dx y' z' y" z"

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Q: .. Find the absolute extrema of the function with its corresponding constrain. a) f(x, y) = x² - y²;…

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Q: Determine if f(x, y) = xe*-y + 100y is increasing or decreasing at (-2,1) if a) we allow x to vary…

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Q: ) Verify the continuity of the function f(x, y) 26– 2x -- y at the point (2,-3).

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Q: Let f be a differentiable function with f(1) = -3, f'(1) =0, and 1+ f(x) h(x) = What is h' (1)?…

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Q: Assume that the functions ?,?,ℎ:ℝ→ℝf,g,h:R→R are differentiable such that  f′(a)=b, g′(b)=c,…

A: given: ℎ:ℝ→ℝf,g,h:R→R are differentiable such that  f′(a)=b, g′(b)=c, h′(c)=d, f(a)=e, g(e)=ℓ,…

Q: F is a differentiable function of two variables, x and y, such that Fx (0, − 2) = −4 and F₁(0, − 2)…

A: Given z=F(tan(u-2v+5), u3v)To find: ∂Z∂u

Q: Find the orginal function of this A Fx) =-1 (B) Frz)= X +1 ニー re Fez) s -x+3 tan x - sec3x

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Q: Using the CRE Theorem, find and sketch the set of all points zo = xo + iyo where f(z) = z² + 2|2|² +…

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Q: Let fbe adifferentiable function satisfying the condition. f(x) for all x, y (+0) ERand f(y)#0. f(y)…

A: Let f be differentiable function satisfying the condition Given f(xy)=f(x)f(y)put…

Q: ) Find an analytic function f(z) = u(xr, y) + iv(r, y) with real part -. -----) u(r, y) = x? – y? +…

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Q: Let f(x, y) ƒ(2, 1) = = 150 - 2x² - 4y2. Evaluate f(2, 1). Give answer in exact form. 138

A: given  f(x,y)=150-2x2-4y2for  f(2,1) , put x=2  and y=1 in f(x,y)

Q: Find the interval(s) where f is concave up for f(x) -4x4-3x- 5x-10 0)

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Q: Consider the function. f(x, y) = 2(y + 1)x² Identify the point(s) on the graph of f at which the…

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: