Find lim r(t) when t→0+ r(t) (4 cos t, 2e', 8t ln t) . 1. limit (0, 2, 0) 2. limit = (0, 0, 0) 3. limit ( 4, 2, 8) 4. limit ( 4, 0, –8) %3D

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A: To show :  lim(x,y)→π4,0tan x cos y = 1

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A: Note:As, per our guidelines we are supposed to answer only 3 subparts if there are multiple subpart…

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Q: 3. i. Find f'(x) if f(x) = 9² + tan='(x²) + In(x® + 2x) + cos I +5*. dy ii. Find dr² at the point…

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Q: f(z) = 7. Use f'(x) = lim e+h-©) to find f'(x). %3D %3D 3z-7

A: The given funciton is:fx=23x-7To find f'x

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A: " Since you have asked multiple question , we will solve the first question for you. If you want any…

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Q: (3) Find the limit if it exists. 1' - ry? lim (a) (z.y)-(0,0) r2 + y? (b) lim (2 + y*) In (x² + y²)…

A: Now we will find the solution of the given limit.

Q: 1 If 3x + 2y = 1 acts as a tangent to y = f(x) at x = and if P = lim x→0 (1) (2) (3) (4) −|2 1 113 1…

A: We can solve as follows we will use the derivative of the function at x=1/2

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A: f:ℝ2→ℝ2 fx,y=x+y , x2+y2 z=1 ,1h=2 ,3 f'x  =lim     h→0fx+th-fxt calculate :f 'z

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Q: 3. (2') Let A+ cos x x 2. Given that q(x) is a continuous function, determine the value of A and B.

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Q: (i) Evaluate In (1-z³) lim 2->0 sin (2z

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Q: 4. L0-dx= (A) lim (3- 4)Ax, (B) lim 3-x)2 (C) lim (3-) 8. (D) lim (3- u)

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