H(x) = L, [At) +A-1) ]dt

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: Determine the equation of the tangent line to the graph of g(x) =| [1- sin(re')] dt at the In z…

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Q: Express the limit as a definite integral on the given interval. [9(x†)3 – 4xj]Ax, [2,9] lim n- 00 i…

A: Express the limit as a definite integral on the given interval.

Q: Suppose f(x) = df Find the derivative dx In(In(In(In(x)))). f' (x) :

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Q: Express the limit as a definite integral on the given interval. [4(x;")3 – 4x;1Ax, [2, 7] lim i = 1…

A: Solve the following

Q: Consider f(x, y) =(ax² + by²). Based on the second derivative test, what are the conditions…

A: Answer

Q: Express the limit as a definite integral on the given interval. lim (5(x)3 – 7x]Ax, [2, 6] n- 00 = 1…

A: Consider the given limit and interval. limn→∞ ∑i=1n5xi*3−7xi*Δx and interval=2,6 Now, go through the…

Q: 2. Calculate the first derivative of f using the forward and backward difference approach in the…

A: The objective is to calculate the first derivative of f using the forward and backward difference…

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: Express the limit as a definite integral on the given interval. lim [9(x;")³ – 4x;]Ax, [2, 8] i = 1…

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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: Find the derivative of y with respect to x, t, or 0, as appropriate. y= In (In 5x) O A. 1 5x ОВ. 1 x…

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Q: Suppose that a nonnegativefunction y = ƒ(x) has a continuous first derivative on [a, b] . LetC be…

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Q: Find the tangent line to the function f(x) = 2x cos4(x) at the point (0,1)

A: We have given function fx=2xcos4x and point 0,1. We have to find tangent line to the function at the…

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

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Q: Express the limit as a definite integral on the given interval. lim [4 – 3(x¡*)² + 6(x¡*)>] Ax, [0,…

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Q: Find the derivative of y with respect to x, t, or 0, as appropriate. y= In(In 9x)

A: The solution for the above question is as shown below.

Q: Express the limit as a definite integral on the given interval. lim (2-5(x,)² + 6(x;")³] Ax, [0, 4]…

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Q: Let f(x, y,z) = z-sin(xy), x t, y Int, z et1. Find derivative of f directly and by using chain rule…

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Q: Express the limit as a definite integral on the given interval. [2 - 5(x,")2 + 6(x,)³] Ax, [4, 8] n-…

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Q: 4. Find the differentiation dy. using definition with limit of the following: y = V2x + 1.

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Q: Consider f(x) = sin(2x) + cos(4x), 0 ≤ x ≤ 1. .......Integrate f over the given interval of x, using…

A: Solution:

Q: I. Find an equation of the tangent line to the graph of 1 t cosh (t² – 1) dt - f (x) = 1 tan-t 1+ln…

A: The given function is fx=∫1+lnx1tcosht2-1tan-1t dt.

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

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Q: Express the limit as a definite integral on the given interval. x; In(1 + x3) Ax, [2, 3] lim 3 dx

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Q: :Show that the function 1 x sin When x + 0 S(x) =- 0, is continuous but not differentiable at x = 0.…

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Q: Express the limit as a definite integral on the given interval. cos(x) Дх, [2л, Зл] X; lim Зл dx 27

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Q: 3. Verify the statement by showing that the derivative of the right side is equal to the integrand…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Determine the equation of the tangent line to the graph of g(x) = | [1- sin(re')] dt at the /In x…

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Q: 2. Show that the function psin(2r) e-*dt g(x) = is differentiable on R and compute its derivative.

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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: Express the limit as a definite integral on the given interval. x, In(2 + x) Ax, [0, 2] lim dx

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: The finite difference approximation of the first derivative in the simple implicit method used to…

A: given  ∂2u∂x2=∂u∂t to find the finite difference approximation of the first derivative in the…

Q: Calculate the derivative e8x d In (t)dt dæ using Part 2 of the Fundamental Theorem of Calculus.…

A: Given To apply the fundamental theorem of calculus first simplify these integrals so that this…

Q: Find the slope of the tangent line to the graph of f(x) = x· 2e*cos-1t dt at x = 1 Jln x

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Q: Express the limit as a definite integral on the given interval. n -Ax, (x;")2 + 6 [1, 5] lim i = 1 5…

A: Given query is to express the limit as definiye integral.

Q: Find the derivative of y(x) = In (7(In(x))* ). %3D (Use symbolic notation and fractions where…

A: Topic = Derivative

Q: Find the local linear approximation of f(x) = tan¯(x – 4) at xo = 5, where Ax = x – 5. Enter the…

A: Given: fx=tan-1x-4

Q: Find the slope of the tangent line to the graph of f(x) 2e'cos-1t dt at x = 1. In x = X'

A: Find the slope with the help of derivative of f(x) at x=1 .

Q: Find the fourth derivative of f (z) = 57 + In (z) – 109z. Enclose arguments of functions in…

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Q: 4. Compute the derivative of f(x) in each part. (a) f(x) = sin(ev) (b) f(x) = (tan r)", x € (0, 7/2)…

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Q: F(x) = x · S, 2e' cos-lt dt at x = 1 In x

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Q: Express the limit as a definite integral on the given interval. lim [9(x;)³ – 9x;14x, [2, 8] i = 1…

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Q: Express the limit as a definite integral on the given interval. x;* -Ax, (x;')² + 2 lim n- co [1, 6]…

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Q: The general anti-derivative of the function f (x) - In(x) is given by x In( x)+ C Inx)-x+ C x In(x)…

A: The integral (anti derivative) of fx=lnx can be evaluated by using integration by parts. The…

Q: Express the limit as a definite integral on the given interval. lim 8x; + (x;)² Ax, [3, 8] dx

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Express the limit as a definite integral on the given interval. lim (4(x")3 – 3x;]Ax, [2, 6] n- 00 i…

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Q: Compute the derivative of h(sin(x)) at æ = 1/6, assuming h'(0.5) 4: %3D

A: As we know that; The Chain Rule: fgx'=f'gx·g'x Let, hfx=hsinx

Q: Express the limit as a definite integral on the given interval. lim [9(x,")³ – 4x†]Ax, [2, 6] n- 00…

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Q: Find the derivative off with respect to x of f(x) = In x⁹. The derivative off with respect to x of…

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