Let f(x) = 3 sin(x). a.) |f'(x)| < b.) By the Mean Value Theorem, |f(a) – f(b)| < a – b for all a and b.

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: Suppose we define a function f(x) by f(x) = a1 sin(x) + a2 sin(2x) +· + an sin(nx), .. for constants…

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Q: Determine the absolute extreme values of the function f(x) = sinx - cosx + 6 on the interval 0 ≤ x ≤…

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Q: Where is the function f(x) is continuous, such that f (x) : In(1-2x)+sin (x 4x+3 %3D [-1, ] – (-) O…

A: We know, ln(x) is defined for x&gt;0. sin-1(x) is defined for x∈-1, 1. f(x)g(x) is defined if…

Q: тт Find the absolute minimum and maximum of f(x) = 2 sec x tan x on the interval [-- 4' 4

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

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Q: 2. If f(x) = cos2x, find f(0), f(--).f),f(-x) 3. If f(x) = x(x+1), show that f(x+h)– f(x)= h(2x +1+…

A: 2. f(x) = cos2x , find f(0) , f(-π/4), f(7π/8) ,                                         f(-x). f(0)…

Q: Show that the function f (x) is continuous on Sin x, r 4 -

A: You have to find the left and right hand limit for the given function.

Q: Find f' (x) for 8 sin(x) f(x) = -; 7x2 – 8 sin(x) s'(x) = |

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Q: On which interval is the function f(x) = tan x² continuous Is the function f(x) = ! - continuous at…

A: 3.1)  tan x2 =sin x2cos x2We know that sin x2 and cos x2  are both continuous functions.Thus, tan…

Q: Find the open intervals on which the function is increasing or decreasing.

A: Given: fx=sinx-1, 0&lt;x&lt;2π To Find: Increasing and decreasing function.

Q: d Prove that (sin-l x) : dx V1 – x²

A: To show that:ddx(sin-1x)=11-x2

Q: Find f'(x). f(x) = O O O 6x - sin² (5x) f'(x) = O f'(x) = f'(x) = f'(x) = = 6-10sin(5x)cos(5x) 2√6x…

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Q: Find the open intervals on which the function is increasing or decreasing.     f(x) = sin x − 1, 0…

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Q: Find the intervals on which ƒ is increasing and the interval on which it is decreasing.

A: Given function is fx=9-x2+sin-1x3.

Q: Find the anti-derivative of g(x) = sec(x) tan(x) which contains the point (TT, 0). O G(x) = -csc(x)…

A: Solution to the anti-derivative can be found by integrating the function.

Q: ) Show that the function f(x) = x 2 − 4x + 3 = (x − 1)(x − 3) satisfies the conditions of the Mean…

A: The Mean Value Theorem states that if a function f is continuous on the closed interval [a,b] and…

Q: Apply the Mean Value Theorem for the function f(x) = 2 ln(4x + 7) over the interval [1,3]. Show your…

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Q: Suppose that f(x) is a continuous function on the interval [0, π]. If f(x)=(sin x)² for 0<x<, then…

A: Since the f(x) is continuous function in [0, π], therefore the value of function at x = 0 must equal…

Q: 4. Verify the Mean Value Theorem for the function y=ln (2x + 3) in

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Q: Q: Show that the function f(x)=- x sin ,X =0 is continuous at x = 0.

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

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Q: For what values of a, m and b does the function x = 0 0 < x < 1 1< x< 2 3, f(x) = -x² +3x + a, тх +…

A: to find the values

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

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Q: (b) Use the definition to show that cosh(-x) = cosh(x). + e-(-x) cosh(-x) e-X + eX

A: Please refer the attached image for complete solution. THANK YOU.

Q: Find the intervals on which ƒ is increasing and the interval on which it is decreasing.

A: Given: fx=tan-1xx2+2 we know that given functionfx is increasing, if f'x is greater than zero and…

Q: 3. Evaluate f x sin2 (x²) dx.

A: Given I=∫x sin2x2 dx To Find I

Q: The Mean Value Theorem can be applied to $f(x)=\tan x$ on the interval $[0, \pi / 4]$

A: The men value theorem states that, For a function f(x) defined on an interval [a, b] such that, (a)…

Q: Find the intervals on which ƒ is increasing and the interval on which it is decreasing. ƒ(x) = -2…

A: Differentiate the function f(x)=-2cos x-x with respect to x to obtain the value of f'(x) and equate…

Q: Let f(x)= x2 + sin x - 2 cos 2x. Find (f-1)'(-2)

A: Given: fx=x2+sinx-2cos2x To find: f-1'-2 Now, we know that f-1x' = 1f'f-1x

Q: Consider the function f(x) = sin2 (x) − sin(x), 0 ≤ x ≤ 2π. Find any x-intercepts of f(x) on [0,…

A: Consider the function f(x) = sin2(x) − sin(x), 0 ≤ x ≤ 2π.Find any x-intercepts of f(x) on [0, 2π]

Q: The derivative of f(x)=sec x is Select one: a. sin x COS X O b. C. O d. sin ² x 2 COS .X sin x cos²x…

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Q: 10. Show that f (x) = { x² sin(1/x) if x + 0 if x is differentiable, but the derivative is not…

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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: Let f(x) = 8 sin-! (x*) s'(x) =|

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Q: Prove that f(x)= sin(5x) < 5x on [0,x]

A: Take the help of derivative and try to prove the given statement in two cases.

Q: If f (x) = - cos(x), then f (10) (x) is equal to (A) - sin (x) ® -cos(x) © sin(x) D cos(x)

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Q: 1) Verify the Mean Value Theorem for f(x)= x+sin(2x) over the interval [0, 2]

A: given f(x) = x + sin (2x)   defined over interval  [0, 2π]

Q: Find the value of K that make the function f continuous at x=2 -4 スー3x+2 sin(nx) + kx + k if x 2

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Q: Verify that the Mean Value Theorem (MVT) applies to the function f(x) = sin? x – cos x on the…

A: Mean Value theorem states that: f'(c)=f(b)-f(a)b-awhere f(x) is differentiable in (a,b).

Q: Apply the first derivative test to indentify all relative extrema. (b) f(x)=x²-2+1 (c) f(x) = cos²…

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: f (x) = 4 sin(3x + 7) is continuous at every point x = x0; that is, lim 4 sin(3x + 1) = 4 sin(3xo +…

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Q: Verify Lagrange's mean value theorem in f(x) = x²+2x-1 in (0,1)

A: We have ,  f(x) = x2 + 2x - 1    We know the , Lagrange's mean value theorem, If a function f is…

Q: (b) Verify that f(x) = 2 cos(x) sin(x). f(x) = sin(7x) + sin(8x) 7x + 7x = 2 sin 2 = 2 sin |co(-)

A: Let the function is  f(x)=sin(7x)+sin(8x)   Formula used: Sin(a)+sin(b)=2sina+b2cosa-b2

Q: Fix a constant r>1 Using the Mean Value Theorem that enx > 1 + x for any fixed x >0 prove

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Q: Find the critical numbers for f(x) = sin2xcos2x

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Q: If f(x)=sin-'x. Show that (1-x2) fx(x)-xf (x)=0. HENCE ,prove that f^(n+2)(0)=n²f^n(0)

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Q: How many integers are there in the domain of the function f(x) = ln (x² – x – 12) + v25 – x² +…

A: The domain of a function is the set of input or argument values for which the function is real and…