x² +1 si x<1 f(x) = x+1 si x21. Is the function f differentiable in 1? draw the graphs f and f'

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: Differentiate the function. y= ln(x3 sin2 x)

A: First, we simplify the given function using the multiplication and power rule of logarithm.

Q: Find the equation of the line tangent to the graph of f(x) = – = -3 cos (x) at x = 3 m(x – xo). You…

A: given: the function f(x)=-3cos(x) the point is x=-π3

Q: sin(x) 19. Evaluate -dxdy by changing the limits of integration appropriately.

A:

Q: 9) Determine the third derivative with respect to x for y = In x 10) Given f(x) 2x + 1 and f(1) 4.…

A: Find the derivative

Q: 9-x2 for -3 Sx S0 f(x) = TCX -x+3 cos for 0 < x <4 Let f be the function defined above. (a) Find the…

A:

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: 10 Find the derivative f'(0) of f(x) = at x + 4 x = 0 using the laws of differentiation.

A: Derivative of the function

Q: If f(x) = x cosh æ + 3 sinh x then f'(x) =

A:

Q: The limit cos(x) +1 lim x – 9T represents the derivative of some function f(x) at some number a.…

A: In the given question, f(x) is cos(x) and a is 9π

Q: 2. Let f(x) = x² ln x + 1. Use the second derivative formula to approximate f"(1) when h = 0.2. %3D

A:

Q: Find the length of the graph of f(x) = ln sec x from x = 0 to x = r/6.

A:

Q: If f(x) = x cosh x + 5 sinh x then f'(x) =

A: Find the derivative

Q: Find the extreme values for f(x) = sin(x) + cos(x) on the interval [0, 2π].

A: The given function is f(x)=sinx+cosx   and the interval is 0, 2π. We have to find extrema on the…

Q: . Does the function cos x x + 0 f(x) = 0, x = 0 have a derivative at x = 0? Explain.

A: Consider the given function fx=1-cosxx        x is not equal to 0x=0

Q: Let f:[-n, 7] –→ R, where f(x) = 2 sin (2x) – 1. TC Calculate the average rate of change of f…

A:

Q: What is the derivative of f(x) =2cos (x)? %3D 2 cos (2x) O -2 cos (2x) O 2 sin (2x) -2 sin (2x)

A: f(x) =2cos2xdifferentiating w.r.t xd(f(x))dx=ddx(2cos2x)

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

A:

Q: Find the absolute extrema of the function on the closed interval. y = 9 cos x,    [0, 2?]

A:

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

A:

Q: If f(x) is odd function, then the derivative of y =sinh (-x)) equals Select one: f'(x) O y'=- V…

A:

Q: Differentiate the function:  k(x) = 4 ln (x) + 2 cos x + x^2 k'(x) =

A: k(x)=4ln(x)+2cosx+x2Differentiate with respect to xk'(x)=(4×1x)+2-sinx+2xk'(x)=4x-2sinx+2x

Q: MY The derivative with respect to x of the function y=-3tan-¹x-(In 3) log, (csc x) is y' = cotx + O…

A:

Q: solve using variation of parameters or reduction of order. (D2 + 1) y = tan x

A: Given (D2 + 1) y = tan x

Q: (a) Evaluate the indefinite integral (anti-derivative) x°(1+ 2*)® dx by using the substitution u =…

A:

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

A:

Q: Find all the relative and absolute extrema of the given function on the given domain f(x) = x^2 +…

A:

Q: 9. S sec³ x tan x dx

A: Given ∫sec3xtanxdx We know that  ∫secx.tanx=secx + c ∫xndx=xn+1n+1+c

Q: Find the absolute extrema of the function on the closed interval. y = 9 cos x, [0, 2n] || minimum…

A: The first and second derivatives of the given function, f(x)=y=9cos(x), will  be given by:…

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

A:

Q: The first derivative of the function h is given by h'(x) = tan(0.1x- x) for -n < x < R. On what…

A: Solution Given h'(x)=tan(0.1x3-x) for -π&lt;x&lt;π.we need to find on what intervals is h…

Q: Prove dx dx 1 f ( sec -x+tan –I 2 1 | f (cosecz) %3D Vsin r sin x

A: Apply trigonometric properties to prove the result.

Q: At which points does f(x) = 2 sin x - cos 2x have an absolute maximum value and what is the maximum…

A:

Q: On the graph of f(x)=sinx and the interval [0,2π), for what value of x does the graph cross the…

A: Plot the graph of sinx given below

Q: Determine the instantaneous rate of change of the function √ sin sin (2³) f(x) = [x² x3 At x=1 dt…

A:

Q: = 1. Use a local linear approximation of the function f(x) = ln(x + sinh(x) + cosh(x)) at some point…

A: Since the required point is 0.001 near to 0, so we approximate linearly about x=0, also at this…

Q: Differentiate the function. f(x) = sin(2 ln x)

A: Chain rule is use to find the derivative of composite functions

Q: Consider the function  f(x) such that (a)  f(1)=1/ln^2 and (b) the tangent line at  (x,f(x))  has…

A:

Q: find the most general ntiderivative f(x) = 4 sec2(x) + 3 sec x tan x

A:

Q: Find the absolute extrema of the function on the closed interval. y = 9 cos x, [о, 2л] (x, y)…

A: Given,

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: Find the relative extrema of f(x) = 1/2x − sin x in the interval (0, 2pie ).

A: Maxima or minima: Let f(x) is any function. 1) Evaluate f'(x) = 0 for critical point. 2) Evaluate…

Q: The second derivative of an anti-derivative of a differentiable function F R-R is: O possibly…

A: The second derivative of an anti-derivative of a differentiable function f:R→R is

Q: 4. The derivative of f(x) = ln x at x = 3 when hpresent = 0.001 and hprevious = 0.002. %3D 5. The…

A: f(x)=ln…

Q: What is the derivative of f(x)=−3cos(x)+4sin(x) at the point x=π/3? Enter an exact answer.

A: Given,  f(x)=−3cos(x)+4sin(x)   We have to find the derivative of fx  at  x = π3

Q: Consider the function f(x)=ln (1+x2). a. Find all the critical values of f(x)=ln (1+x2). Using the…

A:

Q: limit x approaches zero, sin^2x/x

A: Given,

Q: Let "g" be the function given by "g(x) = lim as h approaches 0 of [sin (x+h) -sinx]/[h]". What is…

A: Given  g(x) = sinx Instantaneous rate of change  g'(x)=limh→0sinx+h-sinxh

Q: Find the average rate of change of the function f(x) = = læ + 0x + 8, on the interval x E [-2,0].…

A: Given:fx=x2+8  on the    interval -2,0Average rate of change of the functionAx=fb-fab-aa=-2 , b=0

Q: alue of A can be calculated based on f(x)dx = 1.

A: The given probability distribution function is,

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.