Determine the domain of the function and prove that it is continuous on its domain f(x) = cosx2 / (x2 - 1 )

Q: Use the LIMIT DEFINITION of derivative to find f'(x) if f(x) =; 3x+2 LUse differentiation rules only…

A: Using definition of derivative, the derivative of function f(x) is given by: f'(x)=limh→0…

Q: Determine the domain of the function and prove that it is continuous on its domain using the Laws…

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Q: Use mathematical induction to prove that the derivative of f (x) = xn equals nxn−1 whenever n is a…

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Q: Show that the function is continuous. f(x) = x sinx

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Q: Use the second order derivative test to find local exterma of the function  f(x) =x3-9x2-48x+72 on…

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Q: Q7 Show that f is continuous on (-∞, 0) sinxif x - 4

A: Trigonometric function with sine and cosine in continuous in its domain.    Here in this question,…

Q: Determine if the function f(x)= is continuous -- sin(x) x on the interval I= (0,1).

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Q: Find local maximum or local minimum of f(x)= -sin 2x -x defined on 22

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Q: Find the derivative f'(x): f(x)=x4-x2+sin-1x/3 **4-x2 is under a radical sign!

A: Consider the given function f (x) taking (4-x^2) under the radical sign. Differentiate f (x) w.r.t x…

Q: Show that the function is continuous. (x) = 3x cos 3x

A: Show that the function is continuous. (x) = 3x cos 3x

Q: Find the absolute max and min of the function F(x)= 2sin(x)-cos2(x) on the interval [-π, π]

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Q: Find the intervals of monotonicity of the function f(x)=x+sinx.

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Q: Find f'(a) using the definition of the derivative. if f(x) = Use the definition of %3D derivate…

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Q: Find where the function is continuous, but not differentiable..

A: Given,

Q: Explain why the function f(x)=cos.x-xmust have at least one zero on the interval [0,5]

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Q: Determine the domain of the function and prove that it is continuous on its domain using the Laws…

A: As we can see in below graph that the function is not defined at odd multiples of {pi/4} . So domain…

Q: How do i figure out whether this function is continuous or not (proving it) without given at which…

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Q: compute the derivative.  f (x) = (cos2 x)cos x

A: To compute the derivative.  f (x) = (cos2 x)cos x

Q: Find the derivative. g(x) = cosh(In(x)) g'(x) = ||

A: To determine the derivative of the function.

Q: Use the definition of the derviative to compute the derivative of f(x)=1−3x2f(x)=1−3x2 at the…

A: Use the definition of the derivative to compute the derivative of f(x)=1−3x2 at the specific point…

Q: Apply the first derivative test to indentify all relative extrema. f(x) = cos² (2x)

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Q: Differentiate the function using product rule. f(x) = (2x³ + 5x) cos x %3D

A: Given : fx=2x3+5xcosx

Q: Compute for f '(3) using the limit definition of derivative if f(x) - 6x²

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Q: f(x) = (2x3 + 5x) cos x

A: Given function is fx=2x3+5xcosx. Differentiate using product rule ddxf·g=f·ddxg+g·ddxf

Q: Find the intervals on which f(x) = cos2 x on [−π, π] is increasing and decreasing.

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Q: Show that the function is continuous on  (∞ , -∞).

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Q: The derivative of the function f (x) 3x tan x is Select one: O f'(x) = 3 tan x + 3x sec² x O f'(x) =…

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Q: Find the domain of the function. f(x) = (6cosx)/(1 - sinx)

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Q: Show that the function is continuous on its domain. State the domain. Vx + x cosx

A: fx=x4+x3 cosx The domain is the set of all positive real numbers including zero. That is, the domain…

Q: What are the intervals of monotonicity of f(x) = arctan (2(x-1)) - ln IxI ?

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Q: How would you define f(2) in order to make f continuous at 2? limx→2 x^3-8/x^2-4 show ALL of your…

A: Let's solve limit problem.

Q: Show that f is continuous on (-0,00) sin x if x 4 V

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Q: Is the function 1 >-{ f(x) = √x x3 x < 0 0 ≤ x ≤ 1 piecewise continuous or piecewise smooth on [-1,…

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Q: Find the derivative of f (x) = arcsin (x²). 2x f' (x) = 1-a4 f' (x) V1-x4 2x O f' (x) = V1-a² O f'…

A: Use differentiation of trigonometric function

Q: Find the derivative of the trigonometric function f(x)=sin2x using the limit definition.

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Q: The derivative of the function f (x) = 3 sin“ x is Select one: O f'(x) = 12 cos³x O f'(x) = 12 sin³…

A: dsinxdx = cosx

Q: 4. Show that the function is continuous on (-00, 0). f(2) = {0 x* sin(1/x) if x 01 if x = 0 S

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Q: find the value of c that make the function continuous

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Q: Using method of sub., find the Anti-derivative 1 x In x

A: detailed solution is given below

Q: Find the intervals of monotonicity of the function f(x)=1−sinxcosx.

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Q: Find the derivative of the function. f(x) = tan(5x²) %3D f'(x) = %3D

A: To find the derivative .

Q: Show that the function xsin f(x)%D 0, When x 0 is continuous but not differenti able at x = 0 When x…

A: Let f be a function defined in the neighbourhood of 'a'. Then the function f is said to be…

Q: Explain why the function has at least two zeros in the interval [1, 5].              f(x) = 2 cos x

A: To show the function has at least two zeros .

Q: Find the derivative. Simplify completely. 1. f(x) = 4x³ cos x 2. g(x): Sx-4 In x 3. у sin x 4. f(x)…

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Q: f(x)=√√x at x = 7

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Q: Does f(x) 1-V1-x² continuous on the interval [-1, 1]?

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Q: f(x) = In(sin² x)

A: Given,           fx=lnsin2x

Q: What value should be assigned to f(2) so that the extended function is continuous at x=2

A: Given graph of f(x)

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.