Exercise 3: Find A and B given that the derivative f'(r) is everywhere continuous, and Aa2 Bx 2, x<2 Br2-A f(a) x 2

Q: The limit used to find the derivative is f(t) – f(x) dy dx lim definition %3D t- x

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Q: If the derivative of y = f(x) at x = 2 is equal to " (0 " then y = f(x) is not continuous at r = 2.…

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Q: 1) Given f(x, y) = x derivative of f? which of the following is Əyox the mixed second order par f

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Q: F(x) = f Cos t dt

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Q: Show that the function y=| × | is differentiable on (-o,0) and (O, c0) but has no derivative at x =…

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Q: What is the %ER of the approximate derivative of f(x) = x2ex , using forward-difference %3D approach…

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Q: Find the derivative of the function using the definition of derivative. dy = lim dx Ar-0 Ar Ay 1.…

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Q: Find the linearization of the function F(x)=tan-1(2x)= arctan(2x) at x=0. Then use linearization to…

A: We know the linearization of the function f(x) at x=a    L(x) = f(a) + f'(x)*(x-a)   In the…

Q: If the derivative of y=f(x) does not exist at X = a then y f(x) is not continuous at X = A) True B)…

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Q: Is there a smooth (continuously differentiable) curve y f(x) whose length over the interval 0sxsa is…

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Q: QIFind the derivative of the function f(z, k) = z* – 16k + tanh(z) – 4 csc(k) in terms of z and k ?

A: Dear student  Here is the solution of your query

Q: Define a function f : R² → R² by f 2.у 1. Show that f is differentiable on A = E R² |x > 0, y > 0}…

A: To show that the function f defined as below is differentiable on A and compute its derivative

Q: Compute the derivative of f(x) = (sin x)v , 0 < x < T.

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Q: 2. Using the definition of derivative, prove the following: 1 (a) f^(x) = if f(x) = Vx (b) y= sec? x…

A: To find the derivative using definition

Q: Let f(2) = x* – i(y + 1)°, (z = x + iy), (a) Determine the points where f is C-differentiable, and…

A: Given :-  let f z = x4 - i  y + 13 where z = x + iy (a) The points where f is ℂ - differentiable ,…

Q: / f'(x) sin x dx = 8, / f(x) cos x dx?

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Q: · F(x) = 5* (S₁²¹6 (√₁+ u²) du) dt

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Q: What value for a will make sinx { ,X # 0 2x f(x) = %3D 3D ,X = 0 a continuous function?

A: For a function f(x) to be continuous at x = a,limx→a-f(x) = limx→a+f(x) = f(a)

Q: Find the derivative. (Hint: en a = x) %3D y =S 4 In x et dt O * - 1 4x3

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Q: Find the derivative of f(x) at r = 0 using the definition of the derivative as a limit. %3D Va +I

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Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of • sin ( z) h(x) = |.…

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Q: Find a positive value, c, for x, thot satisfies the Mean valve Theorem for derivatives for…

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Q: Find the derivative of the function f(z,k) = z^4— 16k^3+ tanh(z) — 4 csc(k) in terms of z and k ?

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Q: Find the interval in which function f(x)=sin (log,x)+cos(log,x) is decreasing

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Q: Prove that if the function f : I → R has a bounded derivative on I, then f is uniformly continuous…

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Q: Compute the derivative of h(sin x) at x = , assuming that h' (0.5) = 10.

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Q: d rcos t sin(x²) dx dt

A: Given,            ddt∫1cos t sinx2 dx

Q: If u, v, w are nonzero differentiable functions, then the first derivative of uv / w is

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Q: a*+1 +1 t4 +1 dt with respect to x. Calculate the derivative ol Jsin(x)

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Q: Find the derivative of the function at Po in the direction of A. f(x, y, z) = x2 + 2y2 – 3z?, Po(1,…

A: We can solve this as follows:

Q: Suppose for sume function f we heve its derivative, f'cx) = e*sin(x), on the %3D interval o< x< ar.…

A: fx is a function such that f'x=exsinx on the interval 0&lt;x&lt;2π We have to determine where the…

Q: HW prove That The derivative of Flx)=x-x is if (x) = 3x?1 use definition of devivativeto finid The…

A: Use following mentioned rules to find the derivative of the function. The power rule of…

Q: Compute the derivative of h(sin(x)) at x = T/6, assuming h'(0.5) = 10:

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Q: Compute the derivative of g(x) = cos(t²) dt. O 42 sin(z*) O cos(x*) -42 sin(z*) O 4a cos(a) O -…

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Q: Find the derivative of the following function F(x) = (2t – 1) dt using the Fundamental Theorem of…

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Q: Find the derivative of the following function (2t – 1)* dt F(x) = using the Fundamental Theorem of…

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Q: The directional derivative of f(x, y) at the point (a, b) in the positive y- direction is f (a, b).…

A: Solution: We know that if f(x,y) is a function of two variables x and y, then fx at a point (a,b)…

Q: The function f has a continuous derivative. If f (0) = 1, f (2) = 5, and f (x) dz 7, what is %3D %3D…

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Q: se Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function g(x) : I VR+…

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Q: Calculate the second-order partial derivative of f(x.v) =sin(x³v?) with respect to x and y, that is,…

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Q: Use the definition of partial derivative of a function f(x, y) = 3x² – xy? to illustrate fi and f2 '

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Q: Suppose F(z) = e dt. Use the Fundamental Theorem of Calculus to evaluate the derivative. F'(z) = dt…

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Q: Repeat Exercise 60, except with these derivative boundary conditions: y'(0) = 0, y'(π) = 1. In part…

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Q: Let f(x) = In(1 + 7 x). Find flS(0), that is the third derivative of f evaluated at 0. f(3 !3D

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Q: Let f(x, y) = (x² +(G))°. Determine the directional derivative of f at the point (1 0) in the…

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Q: What is the derivative of f(z) = (z³ –- (z – 1)º)*? %3D

A: Given function is f(x) = (x3 - (x-1)3)3

Q: Use the Second Derivative Test to determine the relative extremum trema) and saddle point(s), if…

A: This is a problem related to maxima and minima of the function. By first derivative test we will…

Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of F (z) = : sin(t) dt…

A: Given query is to find the derivative.