2. Let f(x) = x² + 2x. f(4+ h) – f(4) (a) Simplify the difference quotient and circle your final answer. Note: If you’ve completely simplified your answer, there should be no fractions in it. (b) Solve the equation f (2) = -1 for r.

Q: 2.3 - Can you show the steps to solving this problem? Differentiate. (33) y = (t^3 + 3t)/(t^2 - 4t…

A: Please see the white board for the quotient rule of differentiation. In this case f(x) = f(t) =  t3…

Q: 16) For the function: f(x) = 4x² +6x+1 A) Find the intercepts.

A:

Q: 3. Solve for r in terms of x¡. T4m 2 m Ax 10 m 10-x,* X章

A: In similar triangles , ratio of corresponding sides are equal.

Q: f(x) = -x² + 2r + 15 What is the first (left most on the horizontal axis) zero of this func- tion, r…

A:

Q: 6. y = x2 is a solution for which differentia

A: Introduction: A differential equation is an equation that contains the derivative of an unknown…

Q: y" + y' - 3y = 4sin 2x

A:

Q: 里() t² + 5 1 lim t一+05t2 +6'2t (?, ?)

A:

Q: The profit from producing n quilts per year is given by the function P(n)=−15n^2+270n−840, where P…

A:

Q: 3. Solve for the root(s) of the equation f(x)=3x³-4x²+8x+4

A:

Q: 2r + 4 Solve R(x) 2 0, where R(x) X - 1

A: Replace the value of R(x)=2x+4x-1 in the inequality R(x)≥0. Then solve for x. After substituting the…

Q: Suppose that |(3x4-x2) dx=Ax+Bx³+C, for constants A, B, C. What is the value of C if the curve…

A:

Q: I have the cost function as C(x)=14x+500ln(x+1)+3000 and I'mtrying to figure out the total cost when…

A:

Q: Find f by solving the initial-value problem. f'(x) = 7e* – 6x³, ƒ(0) = 5 -

A:

Q: y = 2x' + 5x from the point (-2,-26) to the point (4,148), you'd have to compute f(x)dx a

A:

Q: Find the point at which the line f(x)=5x+14 intersects the line g(x)=−2x (_,_)

A: Given that,  Line f(x) =5x+14 and line g(x) = -2x intersects. So, both the function gives the same…

Q: Solve for x. Show your work. 4x + 5 = 23 4x - 5 = 8x +7- 6x 6. 5.

A:

Q: B. Find the absolute extremum value 2. y = x* - 8x² + 16:on[-3,1]

A:

Q: 9. At time t = 0, a diver jumps from a platform diving board that is 32 feet above the water. The…

A: Given, The position of diver is given by the equation  st = -16t2+16t+32 At t = 0 ;  st = 32 feet…

Q: solve for y in terms of t or x, as appropriate.

A:

Q: |(3x4–x²) dr=Ax³+Bx³ + C, for constants A, B, C. What is the value of C if the cunrve y=AxS+ Bx³ +C…

A: This is a simple question based on integration which could be solved using the basic knowledge of…

Q: 3. Use the Intermediate Value Theorem to show that there is a solution of the equation, r3³-4x = 1…

A: The given equation is x3-4x=1, (-1,0).

Q: The weekly revenue from the sale of x units of a service is given by R(x) = 192x - 6x thousand…

A:

Q: solve in R the inequation Vx +4 < x + 2

A:

Q: For what value of k will y=2x^2+kx-9 have a minum at x=3?

A: The given equation is,

Q: y' = 2xy²; y 4 – x2

A: Differential equation

Q: Solve using Methods of Undetermined Coefficient (D² – 1)y = x – 1

A: To solve the following problem using method of undetermined coefficients

Q: Find the point on the graph of the line f(x)=3x+4 that is closest to the point (6,3) x= y=

A:

Q: 16 Solve the equation for for y 3rex 1 r2 x - 0

A: 3xex+x2ex=0

Q: The value of x which satisfy 3x + 1| < - is : 5.

A:

Q: Solve (x + 2)x 4 geometrically by constructing a line segment of length x .

A: We can expand it by multiplying x inside bracket then it is parabola equation then draw the parabola…

Q: An equation for the stretched y = x2 -1 vertically by a factor of 3.

A: If we have a function f(x) vertically stretched by a factor of 3 function is g(x): g(x) = 3f(x)

Q: The x-values satisfying that 2x² + 5x – 12 > 0 is:

A: We have 2x2 +5x -12≥0

Q: Solve for the domain and range of. f(x.y,z) = 4-x2-y?

A:

Q: 24. Find the point of inflection of the curve x3 – 6x2 + 2x + 14.

A: Using formula of point of inflection of the curve.

Q: Solve the equation 2x² – 3y² = 6 for y. Is y a func- tion of x?

A: Given equation is 2x2-3y2=6. To solve for y and  to determine whether y is function of x. Solution:…

Q: The line tangent to y = ƒ1x2 at x = 3 is y = 4x - 10 and the line tangent to y = g1x2 at x = 5 is y…

A: The line tangent to y=fx at x=3 is y=4x-10 &amp; the line tangent to y=gx at x=5 is y=6x-27. Put x=3…

Q: The path a diver takes from the diving platform is modeled by the equation f (x) = –,x² + 3x + 12…

A: find the maximum height

Q: Suppose that / (3r-x²) dr=Ax³+ Bx+C, for constants A, B, C. What is the value of C if the curve…

A: The given integral ∫3x4-x2dx=Ax5+Bx3+C

Q: Find the number of units X that produces a maximum revenue R in the given equation. R= 36x2/3 -2x

A:

Q: Find the root of the equation x'-4x - 9 = 0 between 2 and 3 using the secant method & = 0

A:

Q: How do you find X in this problem?

A:

Q: The total revenue in Php received from the sale of x units of children toy is given by R(x) = 3x² +…

A:

Q: 4 f(x) = 2x + 7m (т — х)2

A: For m=9, to to find the extrema of: fx=2x+7m-4m-x2

Q: 02. Solve the DE. y" = x2sinx 2. by using variation of parameters method.

A: Given: y''' = x2sinx.

Q: Use Reduction of Order to find the General Solution: (D2 - 4D + 4) y = ex

A: The objective of the question is determine the general solution of the given differential equation

Q: y" + y' - 3y = 4sin 2x %3D

A:

Q: 3. 2y" + у' %3 А. 3 В. Зx2 С. Зх D. x?

A:

Q: Find the point at which the line f(x)=−5x−10 intersects the line g(x)=−4x−8.

A: We need to find a point of intersection of both the given lines.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.