(@) Explain why f(z) = 5z"- 6+ Zcos z-z'e the function is entire?

Q: What are all absolute and relative extreme values of the function f(x)=– sin z on the interval (0,…

A: Given function f(x) - f(x) = -sinxDifferentiating on both sides with respect to x - f'(x) =…

Q: Find the most general antiderivative of the function.(Check your answer by differentiation.)

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Q: The function f(x) is defined by f(x) =2. What points (x, y) on the graph of f(x) have the property…

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Q: funchoN f whose second derivative is f ")= 5x+2sin(x If fo 3 and fro)= 3. what is fe?

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Q: (8) Find the derivative of the functions (iv)f(x) = e* arcsin x arcsin 3x (v)h(x) = x' arctan 2.x…

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Q: a) Prove that (arctan r 1+2 b) Using part(a), find the derivative of f (x)= arctan (208 )

A: Properties of derivative  f(g(x))=f'(g(x)) g'(x)ddxcosx=-sinxddxax=axloga

Q: 3. Sketch the derivative (i.e., f'(x) vs. x) of following function: 25 20 S 15 10 -2 -1 1 2 (x)f = A

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Q: Find the derivative. f(x) = tanh(x) f'(x) = Need Help? Read It

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Q: Use second derivative test, If f(x) 4x +4 then f(z) has a local maximum at the point %3D I = -3 T= 3…

A: This question is based on maxima and minima of function.

Q: Find the most general antiderivative of the function.(Check your answer by differentiation.)   f ( x…

A: To find the antiderivative of f(x), we integrate it C= integrating constant

Q: (8) Find the derivative of the functions (i)h(x) = sin 2.x cos 2x (ii) f (x) = cos (tan 4.x) 1 =-…

A: We need to differentiate the given function. We will use different method of differentiation . ( As…

Q: (3) A wire 10 cm long is cut into two pieces, one of length x and the other of length 10 - x. Each…

A: Length of wire = 10 cm

Q: Find the most general antiderivative of the function.(Check your answer by differentiation.)

A:

Q: The folowing is a reworded question from very last night . A printed solution of  a length of curve…

A: To find the correct integrand to evaluate the length

Q: The function f is defined by f(x)=x/(x+2). What points (x, y) on the graph of f have the property…

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Q: Find the relative extrema of the function h(x) = 2 tanh x − x. Use a graphing utility to confirm…

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Q: Find the most general antiderivative of the function. (Check your answer by differentiation. f (x) =…

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Q: The maximum rate of change of the function 1 f(x, y) = at the point (1, -2) happens in direction of…

A: I have find the direction and value of maximum rate of change of given function and say that given…

Q: uppose that f(z) is a differentiable function satisfying f(2) = f'(2) = 4. The equation of the…

A: We have f(2)=f'(2)=4.  we have to find the equation of the tangent line on f(x) at x=2

Q: The derivative of a function f is given by f'(x) = esin z On what intervals is f decreasing? cos x –…

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Q: Let y = 5−2x be the tangent line to a function y = f(x) at x = 3 and y = 2+3x is the tangent line to…

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Q: (8) Giry thieo examplos of functions f=IR→ IR is not megasurable. -

A: The objective is to find the example of a function f:ℝ→ℝ which is not measurable. Example:1 Let…

Q: 27 1, 2. -1 1 2

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Q: Find the deriviate of the function using the definition of a derivative. State the domain of the…

A: Consider the given function.

Q: Find the point of inflection and discuss the concavity of the graph of the function. f(x) = sin…

A: Given f(x)=sinx4         , 0, 8π

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 f'(x). f(x) = e\ – x³ arctan(x) f'(x) = %3D Check that your answer is reasonable by comparing…

A: We differentiate the given function with respect to x. On the right side for the term x3arctanx we…

Q: The derivative of the function Ve-tanh a is O y = -sech3x vetanh z 2 O y = -sech?x Ve-tanh / 2 O y =…

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Q: Find the x-value of the extrema by using the Second Derivative Test. Justify your answer. f(x) =…

A: As per the question, we need to find out the x value of the extreme, for bubble 3 only. For (3),…

Q: find the equation of tangent line of function f(x)=csc(x)-cos(x)1/2 at the point ((2*3.14)/3,…

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Q: True or false? The function f(, y) is continuous at x² + y? the origin. O True False

A: We have to check three condition for continuity

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: 2. Use the definition of derivative (as a limit) to differentiate f(x) the rules of…

A: We need to find derivative using definition of derivative. Definition of derivative is given by -…

Q: Find the point of inflection and discuss the concavity of the graph of the function. f(x) = sin…

A: Given- fx=sinx4,0,8...........(1) As we know that inflection point is a point on the graph at which…

Q: he tangent line to y= f(x) at (-7, -6) passes through the point (-9, -2). Compute the following.  a)…

A: GIVEN DATA : Equation y=fx                         Tangent of the y=fx at -7,-6 passes through the…

Q: Only use chain rule, not differentiation pleae given y4-3x=7 please find y' use the below formula…

A: Find the derivative by chain rule

Q: 13. Suppose a continuous function f and its derivative f' have values table. Given that f(1) 2, use…

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Q: How can a linear approximation be used to approximate the value of a functionf near a point at which…

A: Given that the linear approximation.

Q: Find the relative extrema of f(x) = 2+ 90r 5x using both first and second derivative tests. f(x) has…

A: We can find the relative extremum as below

Q: Let f (2) = (4z + 3) (i – 2). What is the real part of the derivative f' (1+ i)?

A: A complex-valued function consists of two parts. The part without i is referred to as the real part.…

Q: Consider the function f(x) = 9x² +3. Its tangent line at x = 6 goes through the points (1, y1) and…

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Q: Find the most general antiderivative of the function.(Check your answer by differentiation.)

A:

Q: Find the most general antiderivative of the function.(Check your answer by differentiation.)

A: Then

Q: Find the most general antiderivative of the function. (Check your answer by differentiation.)

A: We have to find antiderivative of the function and we have to check the answer by differentiation:…

Q: 1 3 + e2 + dx 2 (3х)3 2х2

A: The integral is ∫13x3-32x2+e2+x2dx. Evaluate the integral using u-substitution as follows.…

Q: 5. Find the second derivative of f(x) = arctan(2x"). (You do not need to simplify your answer.)

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Q: Solve the problem using the CHAIN RULE of differentiation    Imagine a sphere whose radius r…

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Q: Determine the sign of the second derivative function as x varies. Where is f' positive? Where is…

A: According to question given thatf"(x)=-4(-3x2+1)(x2+1)3

Q: 5. Carefully explain why 2 arcsin(x)+2 arccos(x) : Hint: How can we tell a function is constant from…

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: