Show that the function f (x) is continuous on Sin x, r< 4 (-0, 00) f(x) = - cos.x, r> 4 -

Q: \S(cos x)dx = 0 %3D

A: Let us consider f is continuous even function. Let f=x2 So, fcosx=cosx2=cos2x…

Q: let f(x)= cos(x)-sin(x)/ h(x)ex, what is f'(x)?

A: Find f'(x) fit given f(x)

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: Is the following function continuous on (-∞, ∞0)? sin x if x x14

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Q: Find the absolute extrema of the function on the closed interval.                    f(x) = sin 2x,…

A: Approach: Without wasting any time, take the derivative of the original function. Find critical…

Q: Find the absolute extremum point(s) of f(x) = e' -Cos x on [-골, T), E any.

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Q: . Show that the following function is differentiable everywhere on R but of which the derivative is…

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Q: What is special about the functions f(x) = sin x - 1 x + 1' x 2 0, and g(x) = 2 tan Vĩ? -1 Explain.

A: Given that functions are f(x)=sin-1x-1x+1, x≥0 and g(x)=2tan-1(x). The graph of the function…

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: Determine values of a and b that make the given function continuous: if x 3

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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: Determine the points in the interval (0, 2T) at which the graph of the function below has a…

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Q: Find the derivative with respect to the independent variable. f(x) = 9 cos x - 2 sin x f'(x) = D %3D

A: We have to find derivatives of function: fx=9cosx-2sinx We know the derivatives of trigonometric…

Q: hich the extrema occur. g(x)=x^2+cos⁡(x^2 ) on [-√π,√π]

A: The function given is gx=x2+cosx2 on the interval [-√π,√π]. To find the extrema of the function…

Q: Find all points on the graph of the function f(x) = 2 cos(x) + cos2(x) at which the tangent line is…

A: Horizontal tangent is parallel to x axis hence slope of tangent is zero at that point

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

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Q: Use the first derivative test to find the local extrema of the following function: f(x) = sin x –…

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Q: Determine whether f(x) is differentiable at x = 0. Show your work. sin(x) cos(x)-1 3x + 1 f(x): = if…

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

A: By the first derivative test, a function is decreasing if its derivative is less than zero.

Q: Find all points on the graph of the function f(x) = 2 cos(x) + cos (x) at which the tangent line is…

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Q: Let f : R→ R be a differentiable function. Then for all x € R, the derivative of f ( sin (4x)) with…

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Q: Find tangent line for the following f(x) = ( 4x² – 3)² f(x) = sin(8 x) at (7, 0) and (T, 1). 9. at…

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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: Use the Second Derivative Test to find all relative extrema. (a) h (x) = x - 2 cos x, [0, 4π]

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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: 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: Q! O show th at [x sin'x + V1-x²] = sin'x sin x

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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: What is the area between the graphs of the functions f (x) = 5 sin x and g (x) = e x − 3, between x…

A: Graph of the given system is:

Q: Let f (x) =x. cos(x2). what is the correct result of the derivative of f with respect to x? A…

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Q: Find f'(x) where f(x) = x*in(#) + (sin(x))".

A: Given that, fx=xsinx+sinxx To find the derivative of this fx=xsinx+sinxx, take the logarithmic on…

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: 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: Evaluate the integral. π f(x) dx   0   where    f(x) =    sin(x)    if  0 ≤ x <  π 2 cos(x)    if…

A: we need to evaluate the integral of πf(x).dx given that  f(x)=sinx if 0≤x≤π/2       cosx if π/2 ≤x…

Q: Find the limit of the trigonometric function.

A: The given expression is limx→0cosx-sinx-12x

Q: IT Evaluate the integral: (cos x + sin x cosx)dx

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Q: Find a nonzero value for the constant k that makes th tan(kx) x 0 Continuous at x = 0.

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Q: Find the function f(x) whose derivatives is sin x and whose graph passes through the point (0,2). O…

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Q: x20 is continuous at x-0, then a = a+sinx If the function f(x): 2+2acosx x<0 a. 1 b. -1 O c. 2 d. -2

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Q: Consider the function f(x) whose second derivative is f''(x) = 9x + 8 sin(x). If f(0) = 2 and f'(0)…

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Q: Use the Intermediate Value Theorem to show that f(x) = 2+ sin r 3 tan x has a | (0. ). solution in…

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Q: If f(x) = x[5 sin (In x) + 2 cos (In x)], find the first derivative f'(x). A. x[3 sin (In x) + 7 cos…

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Q: 5 f(x) %D sin x

A: Given  f(x) = 5sin x We have to check the continuity of the function on the interval [0, 2π].

Q: Find a value of c that makes Continuous extension the function 9x - 3 sin 3x 5x f(x) = c, continuous…

A: The given function is

Q: find the intergral of f(x) = sin(x) + cos(2x) on the interval [0,pi]

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Q: Show that the function f(z)=sin x coshy+I cosx sinh y  is continuous as well as analytic every where

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Q: The graph of f(x) = cos x and a tangent line to f through the origin are shown. Find the coordinates…

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