gubanaT .X 41! J, Ca TTungJ. Given the function m : x→ 3x – 1, and x > TF functions mh : x→ 4x - 3, find the function h.

Q: Find the linear approximation L(x of the function f(x) =V1– at a = 0. L(x)=mx+b where m is - and b…

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Q: Use e – 6 definition and show that the function 4x² – y? if (r, y) # (1, –2) 2r + y f (r, y) = • 4,…

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Q: et f(x) = V42 – x and g(x) = x? hen the domain of ƒ o gis equal to [a, b] for x. | nd || ||

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Q: For what vaļue of x does the function g(x) =x - 2x? strictly convex? В. x> 0 A. x> 2 D. x -2

A: From the given problem:   gx=13x3-2x2   As we know that:   If f''(x)<0. then function strictly…

Q: D. On what point/domain will the f(x, y) = Vx ey will be continuous? Explain your answer!

A: Solved below

Q: Let f be a differentiable function of one variable, and let w = f(p), where p = (x² + y² + z?)\/2.…

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Q: Given the function f(x) = | (t³ – 30t) dt, determine all intervals on which f is -2 concave uр.

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Q: b) Find c within the interval [0,4] such that fave = f(c). Round your answer to three decimal…

A: The average value of a function fx on an interval a, b is given byfavg=1b-a∫abfxdx

Q: Let g(x) = S,"(t² – 3t) dt. On what interval(s) is g concave down? Justify your answer.

A: To find the intervals in which a function f(x) is concave downward solve for f''(x) < 0.…

Q: Estimate the value of f, (1 – r 4.r + 2x) dr using single application Simpson's 1/3 Rule.

A: This is a Numerical Analysis problem.

Q: given f(x,y)=ex^3 . y^8-x8y3 ,show that fxy=fyx

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Q: For what values of a is

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Q: For the function f(x,y,z) = In (8x + 7y+ 10z), find fy, fy, and f,. fx fy =D Iz =

A: given,      fx,y,z=log8x+7y+10z

Q: A clamped cubic splinc spedie for a function ļ on [o,3] is. given by o r x <l sCx) = i+ ax?_- 2x3,…

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Q: Given f(x, y) = et" Y° – a°y°, show that fæy = fyx· 93 fyæ- %3D

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Q: Let f(x) = V42 – r and g(x) = 2? – a. Then the domain of f ogis equal to [a, b] for T. a and b =

A: fog= (42-(x2-x))0.5       = (42-x2+x)0.5

Q: Find the lengths of the functions of x over the given interval. 들+t from x=I tox=3 y = 1) 2) 4) 53…

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Q: Given the function: f(x,y, z) = x°y2² + æy° +y°z Find а. fazy: (x, y, z) b. fazyz(1, –1, 1) -

A: Given the function :  f(x,y,z) = x3y5z7 + xy2 + y3z

Q: On what interval(s) is the function y = –2x² + 3x/3 both increasing and concave down?

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Q: Let f be a differentiable function of one variable, and let w = f(p), where p = (x² + y² + z?)\/2,…

A: In the given question we have to prove the equation.

Q: Given that f(x, y, z) = xy + z and x = s2, y = st, z = t2, find the composite function.

A: To find the composite function.

Q: Given f(x,y) = -5xy2 where x = 4t and y = 8t2. Find f' (t) at t = 1.

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Q: For what value of a is

A: Given           f(x)=x2-1    ,  x&lt;32ax       ,   x≥3

Q: Given: 2x3y4z?w² + 3x²y³z³w6 = 1 where w is a function of x, y, and z. %3D aw Differentiate…

A: We have to solve

Q: Let f be a differentiable function of one variable, and let w = f(p), where p = (x² + y² + z?)!/2.…

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Q: For function f(x,y) to have maximum value at (a,B) IS 1) rt – s>0 and r0 and r>0 3) rt – s?0 and r>0

A: for function f(x,y) to have maximum value at (a,b) is rt-s2&gt;0,r&lt;0

Q: On which interval(s) is the function g(x) = xª – 8x² + 5 concave down?

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Q: O For the function $(x), fla) i defined and lem f Gx) exuts, when is fG) continuous tメO

A: Definition of continuous function: The function f(x) is continuous at x = c when: i) f(c) is…

Q: Let f be a differentiable function of one variable, and let w = f(p), where p = (x² + y² + z?)\/2.…

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Q: Syppose that Ts Cx) centered at a for f(x) is giver by T5 (x) = 3+5(x-2) +8(x-a)?+a(x-2)+ (x-2)5.…

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Q: Consider the function F whose criterion is = / dt. 1+ t2 F(x) sena When determining dF/dx the result…

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Q: Let f(æ) = (4x + 26) In(æ + 3) %3D for æ > -3. Find the smallest value of A so that f(a) is concave…

A: Here we will find out the required condition.

Q: For y=f(x)=x²-2x+7, find dy and Ay, given x=4 and Ax= -0.2. dy=(Type (Type an integer or a decimal.)

A: Use formula and put value

Q: Q3) For what values of a and b are ax + 2b , y = {x? + 3a -b, (3x-5 , 0 2 Continuous at every x ?

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Q: 10.Show that F(x, y) = (1 + xy)e*yi + (ev + x?e*y)j is conservative and find a function "f" such…

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Q: Consider the function f(x, y) = x²y+ y³ – 75y. f has ? v at (0, 0). f has ? at (0, –5). f has ? v at…

A: The given function is  f(x,y) = x2y+y3-75y  We have to find the value of f at  1) (0,0)  2) (0,-5)…

Q: For which values of a ER is the function f(r + iy) = (a²x – axy) + i ax? + ay %3D an entire…

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Q: ax +b. N<2 Given fx) - find a & b such that f is differentiable at 2. 1212-1, x22

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Q: Q4) For the following functions f(x) = e*,g(x) = e¯× in C[-1,1], find ,\lF||, d(f,g), and then find…

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Q: , Consider the function f(x, y) = x'y + y – 27y. f has v at (3/3, 0). f has ? at (0,0). f has ? v at…

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Q: . For what value(s) of c is f(x) = 54-x³, x < 3) %3D lcx² + 13, x 2 3) continuous everywhere?

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Q: de fined as F(X) = P(X f(t) for – a <x < a. - t<a

A: Here f(t) is probability density function of x.  Where -a&lt;x&lt;a.

Q: For what values of a and b is ax + 2b, g(x) = {x? + 3a - b, 0<xS2 3x 5, %3D - continuous at every x?

A: The given function is gx=ax+2b,        x≤0x2+3a-b,  0&lt;x≤23x-5,           x&gt;2. For the given…

Q: the function 2x4jwhen x²+y°+0 Prove that h (a,y) %3D Oj when x=y=0 epect is Variables Lontinuous…

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Q: Show that the function u = 9(ry) + /TY v(y/x) provides the uation ‚²u y? 0. dy?

A: First find the partial derivative of the given function with  respect to x :

Q: of Find of and for the following function. ду 1(x,y) = (2x – 9y)5 %3D of 1 дх of 1 dy

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Q: Let a +b = 4, where a 0 for all x, prove that g(x) dr + g(x) dx increases as (b- a) increases.

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Q: 2. If f(x, y) is a function of y only, then S" S fdxdy Si fdy. %3D

A: Given query is to find statement is true or false.

Q: For which values of a e R is the function ++(). f(a + iy) = (a²z - ary) + i + ay an entire function?

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