The graph Figure 6 is the derivative of a function f which is defined only for 0 < x < c. f b Figure 6 a) Find all the local maxima and minima of f (not f'). b) Find the absolute maximum and absolute minimum of f, or show that they do not exist.

Q: dx 1 = J Jaz-x2

A:

Q: Find the slope of the tangent line to V3x+ 4y= 5 at point (3, 2) %3D Onone of the above O-1 03 O-2 O...

A:

Q: Evaluate the following integrals.

A:

Q: Find the solution of the Linear Homogenous Differential Equation with Constant Coefficients. (D² + 3...

A:

Q: Find f'(x) for the given f(x). (a) f(x) = x8 – 7 /7 + 9x¯7

A: f'(x)=ddx(f(x))f'(x)=ddx(x8-7x+9x-7)f'(x)=ddx(x8)-7ddx(x)+9ddx(x-7)       (ddxxn=nxn-1)

Q: g(x) = e v find the derivative g'(x). 1 2e* 1 cev 2Vx e. B. A.

A:

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) lim x→−3  x2 − x − 12 4x...

A:

Q: ey dy dx e2x – exey

A: Given differential equation can be evaluated as shown below

Q: 00 4 xln?x 00

A:

Q: (2D4 — D3 — D?)у %3D0 - A. y = c1x + cze* + c3xe* + Cze¬0.5x B. y = c1 + C2x + C3e* + c3e¬0.5x C. y ...

A: From the given differential equation: 2D4-D3-D2y=0 The auxiliary equation is; 2m4-m3-m2=0 So, 2m4-m3...

Q: sin x lim In(x* + 1) x + o+ O 4 O +00

A: To evaluate: limx→0+sin xln (x4+1) The form of the limit is 00 form.

Q: What is the value of this summation given by, J=0

A:

Q: (b) A function is defined as f(x) = { U, 2 2 2, 1< a < 2 (i) Sketch the graph of f(x). (ii) Find th...

A:

Q: f(t) = (+ 1. Find the forier tansform of F(1) = (+) for t >0 %3D 3

A:

Q: Find a homogeneous LDE with constant coefficients that has y= - 3xsin2x as a particular solution.

A:

Q: I shift as in Example 4.9 to find the general solu b. (2D – 1)²y = 0 + czx?)e2x

A:

Q: You are given the following frequency distribution of soft drink purchases. Soft Drink Frequency Cok...

A:

Q: 2x3-4x-8 (x²-x)(x²+4)

A:

Q: Which of the following is an inflection point of f(x) = 3x - 20x3 %3D

A: We need to find the inflection point of f(x)=3x5-20x3

Q: Evaluate the integral. f32 d= -2 dx +C %3D NOTE: Enter the exact answer.

A: Let's find. 

Q: dy (x+y)² 4 dx X- 2

A:

Q: Find the indefinite integral. (Use C for the constant of integra 2 xp xV4 - (In x)2

A: Solution

Q: Find the limit. (If an answer does not exist, enter DNE.) sin 0 lim 0 → 0 40 + tan 0

A: Given limit is in indeterminate form , just use the L'Hospital's rule and find the required limit of...

Q: The bounded by y= xx*+1, area of the region axis. y=x, x-- 3, and

A:

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. ...

A:  

Q: Find a homogeneous LDE with constant coefficients that has y=e+ 2e-x as a particular solution.

A: Homogeneous LDE with constant coefficient :   A Linear differential equation with constant coefficie...

Q: Find the integral. (Use C for the constant of integration.) (x6 + 5-×) dx

A: In this question, we need to find the integral of given function.

Q: 3. SET UP the definite integral that will give the area of the shaded region using a. y as variable ...

A:

Q: A system of 2 ODES with initial conditions is given as follows. У 3 бу — У2, Ут (0) %3D 1 y, = 2yı +...

A:

Q: Given that lim_f(x) : X→3 lim g(x) : lim h(x) = 0, X→3 = 4 = -4 X→3 find the limits, if they exist. ...

A:

Q: rdr a. V /x+3

A:

Q: (2a² +3a +11) a-5 lim a2 +3a-7 In a 00 a+10

A: Solution is here

Q: Inverse matrix (Pi). Give elements rounded to four decimals. P11 = P12 = P13 = P21 = P22 = P23 = P31...

A:

Q: csc[In(tan e4*)] CsC y = coth[In(1-x)1/3]

A:

Q: f(x) = x2 - e* 5 Find the value of x for which the second derivative f'(x) equals zero.

A:

Q: Check that y Cx) = e* is the Solution of y" + y' - 2y = 0

A:

Q: SADT] The length l, width w, and height h of a box change with time. At a certain instant the dimens...

A: Topic = Area

Q: Consider the following curve. y = 2x2 − 4x + 1 Find the slope m of the tangent line at the point  (3...

A:

Q: Consider the function below. C(x) = x'/5(x + 6) (a) Find the interval of increase. (Enter your answe...

A:

Q: A sinusoidal curve y = a + b sin(cx) where a>0, b>0 and c>0, has 2 concurrent maximum points at coor...

A:

Q: 5. Derive the general solution of x cos? y dx + tan y dy = 0

A:

Q: 1

A:

Q: Transposed matrix (n¡) n11 = n12 = n13 = n21 = n22 = n23 = n31 = n32 = , N33 =

A:

Q: sec?y = x3 – 2x tan y dy dx

A:

Q: u = Vx + 5 (x + 1) then du/dx is Зх — 11 Зх + 11 2 Vx + 5 2 Vx + 5 A 3x + 10 Зх — 10 2 Vx + 5 2 Vx +...

A:

Q: Find the integrating factor: (2x^2+y)dx+(x^2 y-x)dy=0

A:

Q: The process of finding the derivative of a given function is equivalent to a. determining the inst...

A:

Q: Find the general solution of y""- 5y"- 6y'=0

A: The given differential equation y'''-5y''-6y'=0

Q: b) Use implicit differentiation to find for the equation yz? -e** cos (4zx)–3y² =4. F. DO NOT use th...

A:

Q: A closed rectangular box whose length of its base is twice as long as its width has a volume of 36,0...

A: Topic = Application of derivative