2. Find the intervals of increase or decrease. a) ƒ(x)=x ln x b) f(x) = xe* c) f(x) = xe¯* d) ƒ(x) = x + sin x

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

A:

Q: | Example 8.12. Use the Trapezoidal rule to estimate the integral exª dx taking the number 10…

A:

Q: Evaluate S sinh x cosh x dx by introducing u-sinh x

A: Given that: ∫sinhx.coshx.dx

Q: find the length of the curve y = arcsin e^(-x) from x = 0 to x = ln 5/4

A: Given curve, f(x)=arcsin e-x from x=0 to x=ln54

Q: | 35. Prove the reduction formula for n > 2: cosh" x dx = cosh"- x sinh x + cosh" п-2 хdx п n-1 п п

A:

Q: the

A:

Q: Limit as x approaches 0 1-cos(x)/sin(x)

A:

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: limit x to 0 sin(4t)sec(1000t)/10t

A:

Q: 1. Evaluate. a) lim x--2 ³-2x² +12 x² +1 x² -8x+7 b) lim x-7 2. What is the average rate of change…

A:

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

A:

Q: The derivative with respect to x of the function y = 3tan ¹x - y' = cotx O the above (In 3) log3…

A: Given y=3tan-1x-ln3log3cosecx

Q: 3. Let f(x) =x In(x – 3)+5. Find the equation of the line tangent to the graph of f at the point…

A: Given thatf(x)=xln(x2-3)+5f'(x)=ddxxln(x2-3)+5         =xddxln(x2-3)+ln(x2-3)ddx(x)+ddx(5)…

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: find a linearization at a suitably chosen integer neara at which the given function and its…

A: Given         f(x)=sin-1x , a=π12

Q: Lim as x approaches 0  1-cos(5x)+sin(3x)/x

A:

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

A:

Q: (A) Prove that: cosh x + sinh x = e*

A:

Q: Use forward-difference formula to evaluate the first derivative of y = cos(x) at x = cos(x) at x =…

A: Given function is y=cosx. We have to evaluate the first derivative of y=cosx at x=π4 using a value…

Q: Plot f (x) = ln x − 5 sin x on [0.1, 2] and approximate both the critical points and the extreme…

A:

Q: (ii) Show that 1 d (tanh-1 x) = dx 1- x2 Hence, or otherwise, show that, 27 tanh-1x dx =- In 4 2. 1…

A: Evaluate: and

Q: Find the equation of the tangent line to the function f(x) = In(5x) at x = 2. (Use symbolic notation…

A: Given that, f(x)=ln5x To find the equation of tangent line to the function f(x)=ln(5x) at x=2.

Q: 8. The value of f sinh* x cosh³ x dx

A:

Q: 3. Prove that: cosh x - sinh x = e¯*

A: Proved Coshx - Sinhx = e-x

Q: 1 3), sinh(x)-cosh(x) dx

A:

Q: 5. Find all x-values in which your function has horizontal tangent lines, f(x) = 2 sin x + x. given…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: In the function:  f(x)= (3x^2)ln(x) , x>0 Where is the function increasing and decreasing in…

A:

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

A:

Q: 4. Find the first derivative of the given function using the Rules of Differentiation: sin x 2x-x-1…

A: We have to solve

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: 24. Estimate instantaneous rate of change of each function at the given x value using a centered…

A: Given :-  The instantaneous rate of change of each function at the given x value using a centred…

Q: Find all points with x-values on (0, 2π), where tangent line to the graph of f(x) is horizontal.…

A: Find all points with x-values on (0, 2π), where tangent line to the graph of f(x) is horizontal.…

Q: limit x to 0 3x-3xcox/sin^2(3x)

A: Here given limit as Use the L'hospital rule which states

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: = 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: Find the equation of the tangent line to f(x) 16e* cos2(x) at x 4 (Use symbolic notation and…

A: To determine the equation of the tangent line.

Q: 5) Use the tangent line at x = 9 to approximate the value of the function f(x)= Vx at x= 8.8.

A:

Q: 6. Find f(x) if f(1) = 1 and the tangent line at (x, f(x)) has slope f(x)

A: Slope of tangent is obtained by derivative of the function f(x).

Q: 4. Compute the derivative of f(x) in each part. (a) f(x) = sin(ev) (b) f(x) = (tan r)", x € (0, 7/2)…

A:

Q: In (sinh x ), + tanh x j + 1-x k )dx 1- sinx

A:

Q: Q1) A) Find the tangent equation for the function: f(x) = Vx² + 5 at =2 ? B) Find the limits by…

A:

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: 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: a(cos2x) sin(x-) TC 1. f(x) = tanx 4. What values should a and b take for the function fx) to be…

A:

Q: 7. Use the limit definition of the derivative to find f'(x). Then find the equation of the tangent…

A:

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

A: The given probability distribution function is,