f(x, y) = 1/² (x² (x² + xy) 0

Q: If f"(x) = t"(x) for 0 < x < 1, then f(x) − t(x) for 0 < x < 1.

A: It is given that f''(t)=t''(x) for 0<x<1. It is known that derivative and integration are…

Q: We study endurance in marathon runners and sprinters. We calculate a z-score for the difference…

A: Introduction Hypothesis is an assumption that is being tested.

Q: Let f (*= {(8) +f(9) for real values of x and y. If f '(0) exist 2 2 and equals –1 and f(0) = 1,…

A: Introduction :

Q: If zis implicitly defined as a function of x and y by xy-yz+xz=0, find dz/dx. (y+z)/(y-x)…

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Q: 1 If y = V1-x then y' = 2/1-x

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Q: 3. lim,10 Vx – 1

A: The limit of any function is defined for any function F(x) on any interval that contains point at…

Q: 3. Find f'(x) for f(x) = 3x-4 2x+3

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Q: 2. Determine f'(1) for the function f(x) = (8x – 6Vx5 + 3) (x² – 9x² +) -

A: A detailed solution is given below

Q: Let f be a differentiable function such that 2 < f'(x) < 4 for all values of x. Show that 10 < f(12)…

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Q: 7. Is the function given by G(x) at x = 2? Why or why not? 1 x² - 6x + 8 continuous

A: Theory : If A function f(x) is continuous at some point a, then it must satisfy All of these…

Q: 2. Find the derivative of f'(x) if ƒ(x) = x*+3x-V x2+x

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Q: The function f(x)=(x)/(x-1) is discontinous at x=1 because

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Q: Find the approximate integral of the following function using Simpson's 3/8 rule and determine the…

A: Given: fx=ex2, x=0, 4, E=0.0002 To find: n To find: Approximate integral.

Q: determine the value of the parameter a that will make the function f(x) = [ax+1, x- -1

A: The given function is fx=ax+1,    x&lt;-1x2-3,     x&gt;-1 To find: Value of parameter a

Q: f (æ, t) = e-t function fea - fu = 0 provides equality. True False

A: Given the function fx, t=ex-t We need to check the validity of fxx-ftt=0 to get the correct option.

Q: Show that the function f(x) = K. when xw0 when xois discontinuous at x = 0.

A: Solution

Q: f(x) = x² - 2, x + 4, O true false x 3 is continuous everywhere.

A: f(x) = ( x2-2, x&lt;=3            x+4, x&gt;3

Q: 3 Let f(x)= x³ - 2x+: Calculate by definition f'(1). X

A: given function to find the derivative

Q: Is the function given by g(x) = x²-3x continuous at x = 4? Why or why not?

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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) = x √ √2+1 dt. Find F"(1) 3

A: Given: F(x)=∫3x t2+1dt Leibniz integral rule for differentiation states that ddx∫a(x)b(x)…

Q: The interval over which the function f(x) = becomes continuous is %3D x+8 (-3, 0) (-3, 3) (-00,…

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Q: Si s(2x)dx = 23. If f is a continuous fiunction and if F'(x) = ƒ(x) for all real numbers x, then (A)…

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Q: 3. Let f(x) = 4x3+ + 2vx-7. Find f'(x).

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Q: Is |3x-1| a function?

A: A relation is said to be a function only when every point in the domain has a unique value in the…

Q: If a = 1 − v^2 and both x and v are zero when t = 0, show that x = −1/2ln(1-v^2) and hence find v^2…

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Q: 5. Determine f,(x); f(x) = x*², x > 0

A: We need to find out first partial derivative

Q: calculate the value of coth-1(x) when x is greater than 1

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Q: 3. Over which interval is the function f (x) = 1 + 2ex -3x increasing?

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Q: compute (x2 - 8x +20) dx on the interval (0,1)

A: To evaluate the given definite integral over the open interval (0,1)