Consider the functions below. F(x) = f(t) dt 4 + u du f(t) %3D Find F"(2).

Q: Use the graph of f to find the interval(s) on which f is increasing, Where applicable, use interval ...

A: A function is said to be increasing if the output of the function increases with value increases wit...

Q: Explain the Systems of Differential Equations?

A: We have to explain system of differential  equation.

Q: Graph each side of the equation cos x + cos 2x = cos 3x in the same viewing rectangle. If the graphs...

A: To Graph: Graph each side of cosx+cos2x=cos3x in same viewing rectangle.If the graph appears to conc...

Q: find δƒ/δx and δƒ/δy. ƒ(x, y) = (x3 + ( y/2))2/3

A: Given: fx,y=x3+y223 To Find: δfδx and δfδy. Concept: a. fgx'=f'gx·g'xb. ddxxn=nxn-1

Q: For each of the following composite functions, find aninner function u = g(x) and an outer function ...

A: y=f(g(x))=tan 5x2Formulaf(g(x))'=f'(g(x))*g'(x)

Q: 7-8 - Yes or No? If No, give a reason. 7. (a) Is the expression () equal to ? (b) Is there a differe...

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

Q: prove it 5. 2 sin (3x) = 1– cos(6x)

A:

Q: Solve the initial value dy/dx = 1/x2 + 1 - 1, y(0) = 1

A:

Q: Find the exact value of tan-1 (-1).

A: Given  tan-1 (-1)

Q: 3. The cost, C, of air conditioning your home, in dollars per day, when the temperature outside is T...

A:

Q: find Ly for the given differential operator if (a) y(x) = 2e3x, (b) y(x) = 3lnx, (c) y(x) = 2e3x +3ln...

A: L=D2-x2D+x a). yx=2e3x Now, Ly=D2-x2D+x2e3x=D22e3x-x2·D2e3x+x2e3x=D6e3x-x2·6e3x+2xe3x=18e3x-6x2e3x+2...

Q: EXAMPLE 2 Solving trigonometric equations Solve the following equations. a. V2 sin x + 1 = 0 b. cos ...

A: Given:a. 2 sinx+1=0b. cos 2x=sin 2x

Q: Determine whether the graphs of the following equations and functions are symmetric about the x-axis...

A: Given: fx=x4+5x2-12 for finding symmetry of given function, we draw graph of given function as below

Q: Let u = 2i - j, v = 3i + j, and w = i + 4j.Find specified scalar (4u) . v.

A: The vector are given as, u=2i-j , v=3i+j and w=i+4j. To find: the value of 4u.v Solution: The value ...

Q: The formula for converting Celsius temperature, C, to Fahrenheit temperature, F, is F = (9/5) C + 32...

A: Given, Temperature range (in Fahrenheit) =41° to 50° Or 41°≤F≤50°

Q: Factor the difference of two squares : x4 - 16

A: We have to factorize the difference of two squares: x4-16 We know that 16=4×4=42 and law of exponent...

Q: Solve using the quadratic formula: 3x2 - 2x + 4 = 0.

A: Given: 3x2-2x+4=0

Q: Table look-up integrals Use a table of integrals to evaluate the following indefinite integrals. Som...

A: It is given that  I=∫exe2x+4 dx                       ……(1)   Substitute ex=t  exdx=dt We get  I=∫dt...

Q: In the theory of relativity, the Lorentz contraction formula              ______________L =L0 √ 1 - ...

A: Given equation is L=L01-v2c2.

Q: The total derivative of f(x,y) = e2x +5y is df =

A: Consider the following function: fx,y=e2x+5y Total derivative of function: df=∂f∂xdx+∂f∂ydy=∂∂xe2x+5...

Q: Find an equation of the tangent line to the graph of the function at the given point, (a) use a grap...

A: consider the given function, fx=2x34 to find the equation of the tangent line first find the slope o...

Q: Determine whether the graph of y5 = x3 is symmetric with respect to the y-axis, the x-axis, or the o...

A: Given function is y5=x3 Now, replace x→-x y5=-x3=-x3 On replacing x→-x function is not same.So, func...

Q: Find fx, fy, and fz, and evaluate each at the given point.                                          ...

A: the given function is: fx,y,z=xyx+y+z the given point is (3,1,-1) we have to find fx, fy and fz and ...

Q: Write a function in slope-intercept form whose graph satisfies the given conditions : Passing throug...

A: To write a function in slope-intercept form whose graph satisfies the given conditions: Passing thro...

Q: Find the derivative of  f(x) = (x^2-5) (x+7)

A: We have to find the derivative of  f(x) = (x2 - 5) (x + 7) We know that if f(x) = uv ,  then  f'(x) ...

Q: Verify that the Intermediate Value Theorem applies to the indicated interval and find the value of c...

A: fx=x3+8,  -9, -6,  fc=6 Since the cube root function is continuous everywhere, therefore given funct...

Q: f(x) = 4x2 at (-2, 16). Solve, a. Find the slope of the tangent line to the graph of f at the given ...

A: Given: fx=4x2 at -2,16

Q: Write an equation involving a, b, and c based on the following description:When the value of x in y ...

A: It is given that the value of x in y = ax2 + bx + c is 4, the value of y is 1682.

Q: The polar coordinates of a point are (−8, 0.75) . Plot the point and find the corresponding rectangu...

A: Given point in polar coordinates is -8,0.75. Points in polar coordinate is given as r,θ. Here, we ha...

Q: Explain what it means for a curve to be parameterized by its arc length.

A: Explain what it means for a curve to be parameterized by its arc length.    

Q: Prove that lim -- (x + 1)

A: we have to prove that: limx→-1-5x+13=-∞   L.H.S: limx→-1-5x+13=limh→05-1-h+13=limh→05-h3=limh→05-h3=...

Q: What is the greatest integer function?

A: The greatest integer function is defined as the function that round-off the real number down to the ...

Q: If c > 0, |u| = c is equivalent to u =_________ or u =_________ .

A:

Q: Solve the logarithmic equation log2(x - 3) + log2 x - log2(x + 2) = 2. Be sure to reject any value o...

A: To solve the logarithmic equation 

Q: Find limx∞ h(x), if it exists, f(x) = 5x3 − 3                                                       ...

A: Given: fx=5x3-3  

Q: 1 Domain Find the domain of the function. 55. f(x) 56. f(x) = x - 3 Зх — 6

A: Domain: 55.f(x)=1x-3At x=3 the function f(x) will be discontinuous.So the domain of f(x) is (-∞,3)∪(...

Q: graph the integrands and use known area formulas to evaluate the integrals.

A: To evaluate: ∫-111-xdx. We know that, x=-xif x<0xif x≥0 Therefore, ∫-111-xdx=∫-101--xdx+∫011-xdx=...

Q: Find T(2). T(2) = 1.0607 Interpret your answers. After two hours, the rate of decrease of the patien...

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