A critical point xo, Yo of a function f is obtained when O Vf(x0, Yo) = 0 or Vf(x0, Yo) does not exist O Vf(x0, y0) does not exist O f(r, y) = 0 x O f(ro, Yo) > 0 O Vf(xo, yo) = 0

Q: Q2/ A/ plot the function Z= 3(1-x) e-x²-(y+1)² – 10(x – x³ – y5)e-x²-y² _ ! e-(x+1)²-y² where…

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Q: Show that the equation Fu 1 u 0x² ² 3t² 0 is satisfied by u=f(x+ct) + F(x-ct) where fand F are…

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Q: The function f (x, y) = x² + xy - x + y² + 7y+29 has exactly one critical point. What is it?…

A: Given that the function fx,y =x2 +xy-x+y2+7y+29    .

Q: Prove algebraic ally that any function of the form f(x)=ax2n+4 (where n is an integer) is symmetric…

A: The given function is fx=ax2x+4. To prove fx=ax2x+4 is symmetric to the y-axis, it is enough to…

Q: The functions f₁(x) = x² and f(x)=x³ are orthogonal on the interval [-3,3] ? True False

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Q: Show that f[x0, x1, x2] = f[x2, x1, xo].

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Q: Suppose that f(æ, y) = e" = e-3z? - 4y? +y

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Q: f(x) = 8+x 8 - x on [4, 6].

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Q: Q3) If f(z) is analytic function and u(x, y) = x3 – 3xy find f(z)

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Q: iven f(x, y) = 100x + 80y - 3x² - 5y² - xy valuate f(7,6) =(7, 6) =

A: Given query is to find the value of the function at indicated point.

Q: True or False.   If f(x) = a * x ^ 3 + b * x ^ 2 + cx + d where a 0, then f has at least one…

A: Given that: f(x)=ax3+bx2+cx+d, a≠0

Q: Let f(x, y) /150- 4а2 — 2у? 4x? – 2y? Evaluate f(1, 3)

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Q: Find x-intercepts of the function: x2 – 9 f (x) = Зх + 1 Select one: O a.x = 3 O b.x= -3, x= 3 C. X=…

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Q: If then fyy = Select one: O True O False f(x, y) = 2(x² + x) (x - y)³ x² + y x - y

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Q: IfY C X, show that inf (X) < inf (Y)

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Q: Suppose f(x, y, z) = xyz + 2xy + 2² · Compute the following values -(2,8₁16) - (-2,-8, 16) (1,-1,0)…

A: We have to find functional value.

Q: Q21) One of the following is correct for functions the f(x)=1,g(x)= x³ and h(x) = ln(x): a) f(x),…

A: To check the linear independence we shall find the Wronskian for the given three functions. To find…

Q: The domain of

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Q: Evaluate the function of x

A: Step 1:

Q: Find the absolute maximum value of f(x) = x² – 2x + 12 over the interval [0, 4]

A: Use critical value and end points for absolute maxima and absolute minima.

Q: What is the point of intersection for f(x) = 2* and g(x) = A (1,) (0,1) C (1,0) (2,4)

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Q: Show Vx Vy[p(x, y) → ¬p(y, x)] E Vx¬p(x, x)

A: Please check the answerin next step

Q: Which one is one of the critical points of the function f(x, y) = 2x + 2y + 8x - 4y + 11? Select…

A: Solution is given below:

Q: e +1 Differentiate the function f(x)= In 5x +1 Se+1 3ex+1 Sesz e3x +1 ,5x +1 e 3e3z Sesz e3x +1 5x…

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Q: a) f(x,y) = x³ + y³ + y(3x²y+ 3ry²) b) f(x,y) = x² + iy³

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Q: Suppose the point (-3, 10) lies on y = f(x) and the point (2, -3) lie point on the function y =…

A: Introduction: The function f(g(x)) or (f ∘g) represents the combination of functions f(x) and g(x),…

Q: If f(x) = x + 9 – x and g(u) = u + V9 – u, is it true that f= g? Yes No

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Q: find a function f for x>0 so that f(x,y)=yf(x)+yf(x)

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Q: Let f(x) Find f(-4) = Sx² +5 (5x2 +5 कर x < 1 x ≥ 1

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Q: Show that the function f(x)=√x+1 is differentiable in 2 = 2 but not differentiable in x = −1.

A: Given data:- The given function is, fx=x+1

Q: 2х f(x) = ,x 1

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Q: Find a,b to continue the function at x=3 if: x > 3) x = 3 x < f(x) = ax + b 2ab + 1 bx - a +3 3)

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Q: 3x + 11y af If f(x, y) = then is : 3x – 11y dy - 66x (3x + 11y)² 66x (3x – 11y)² 66x (3x + 11y)2 66x…

A: Partial derivative

Q: Determine the type of functions from R to R with necessary figure. i) f(x) = 5x + 7 ii) f(x) = (x² +…

A: (i) fx=5x+7 This function is state line and has roots is x=-75

Q: Let f(x) = Vx and g(x) = x³ +1. Find 29 a) f(g(2)) b) g(f(4)) c) f(F(16)) d) g(g(0)) e) f(2+ h) f)…

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Q: Let f(x, y) = √175 – 3x² – 4y² Evaluate f(5,3)

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