Using the formula f'(x) = lim h→0 f(x + th)-f(x) t and admitting the existence of the derivatives of the functions considered here. Calculate f'(z) . h, where: f: R³ → R³, defined by f(x, y, z) = (x², y², 1+y+z²), z = = (1,0,0), h= (1,1,1)

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Q: %3D

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A: Given, limh→0 2hh2x+2h+2x The definition of derivative is given by fx=limh→0 fx+h-fxh

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A: According to question that :y'=-x2+1x2-42

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A: given                  f(x)=4x+7

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Q: (a) Find the slope m of the tangent to the curve y = 8 + 5x² - 2x³ at the point where x = a. m= (b)…

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Q: Let f(x)=x²+x. Compute f'(2) using the definition of the derivative, f(a+h)= f(a) f'(a)= lim h 0 h

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Q: Use the definition ƒ'(zo) = lim Z→>>> ²0 1 derivative of f(z) == for z = 0. Z f(z)-f(zo) Z-ZO of the…

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Q: 1. f(r +h)-f(r) Using f'(r) = lim %3D Find the derivative of f(r) = V3x- 4. %3D

A: To find the derivative of f(x)

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A: First we will it's derivative then put x=2 then we will find tangent equation

Q: Compute the derivatives of the fallowing functions. use any rule but explain what ar methed, did No…

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Q: det R have the inner Euclidian fipace product 4=(5,-1) and let X= L1,1) and Find l lyll and Kxy>…

A: Given that x=(1,1) and y=(5,-1)

Q: Using the formula f(x+th)-f(x) f'(x) = lim h→0 and admitting the existence of the derivatives of the…

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

Q: (6) Find the derivative where it exists (c) Where is flz) analytic ?

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Q: 2. Use the derivative rules to find f (x). (a) f(x) = (2x® – 8x-2 + 9) +) 3 (b) f(x) = COS x CSCX_…

A: Find the derivative

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Q: Find the derivative of the function f(x) = 4x2 – 13x – 30 by definition of derivatives f(x + h) –…

A: We have to find the derivative of the given function: fx=4x2-13x-30 by the definition of…

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Q: Using the formula f(x+th)-f(x) t f'(x)= lim: h→0 and admitting the existence of the derivatives of…

A: a) f:R3→R2 defined by fx,y,z=x2+y , x+y+z2 also given z=1,1,2 , h1,1,2 using the formula…

Q: 1 (d) Last week, Amy walked a median of 7.5 kilometres each day. 1 kilometre = 0.6 miles The table…

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