Use the fundamental theorem of calculus for path integrals to evaluate f.(yz2, xz2, 2.xyz). dr where c is the path parameterized by 7(t) = (2t + 1, 3t + 2, t + 1) with 0

Q: Show that the directiona f(x, y, z) = z²x + y ² at ( X (1/15" + ) ; 255. them

A: fx,y,z=z2x+y3 P1,1,2v→=15i+25j We know directional derivative Dv→fP=∇fP.v→v→

Q: Differentiate f(w) = sinw + w²tan-1w

A: We have to find differentiation of given function.

Q: 2. Use the First Fundamental Theorem of Calculus to differentiate the function f(r) = VI+ tª dt.

A: We will use the first fundamental theorem of calculus to evaluate the derivative.   The detailed…

Q: Assume that f is an odd function defined on R and t e Rt. Compute

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Q: kh= •a+h [ath 2xƒ(1) √ √ 1 + (ƒ' (1))² dt 2лf(t).

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Q: Suppose you have just poured a cup of freshly brewed coffee with temperature 95°C in a room where…

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Q: Let f(x, y, z) = 5x³ - y³ + z². Find the maximum value M for the directional derivative at the point…

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Q: Evaluate ∫ ▽f*dr Where f(x,y,z)=cos(πx)+sin(πy)-xyz and C is any path that starts at (1,1/2,2) and…

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

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Q: 15. Differentiate 4y³ with respect to x. A) 12y? B) 12y C) 12y2 dy D) 4y2 dy dx dx 16-17. Find the…

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Q: Pron a. If u = f(x, y), where r = e' cost, and y = e' sint, show that (3)³ + (3) ² - - ² [(-)* +…

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Q: 13 Find the linearizatian z=L(x.y) f the function 2=f(x.y) =4x²-y²42y at the point (x.y) = (3,2).…

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Q: Consider the function f(x) = x ² + 3. Part 1: Compute the slope of the the tangent line to y = x2 +…

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Q: Give an example to show that X' need not be separable if X is separable.

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Q: Prove that f (z) =zz is nowhere analytic

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Q: of lf" (x) [0,2] f(x)=√1+x² HINT: Much like the previous question except that you are focussing only…

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Q: (z)dz

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Q: Use the second fundamental theorem calculus along with the chain rule to find sint dt dx sinx 2x…

A: We have to find          ddx∫1xsint dt using the second fundamental theorem calculus along with the…

Q: What is the equation of the tangent plane to the graph of 3x²+4y²-2²=3 at the point (1,1,2) ? 03 1…

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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: Determine each of the following derivative values that involve functions that are defined in terms…

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Q: 6. For which positive integers n > 2 can V2 be constructed? Justify your answet

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Q: 7. F- dr from (0,0) to (3,9) along the curve y=x' if F(x, y, z) = 4 xyi + 3xy'j Evaluate

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Q: f(t) = mt + b+ A sin-

A: Given data:     The given price of the model is: f(t)=mt+b+Asin(πt/6). The given price on the first…

Q: Find whether the function F= 5yz? i+(3x– 2)}+(x² – xyJk is solenoidal.

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