Find the following using the table below. 1 2 3 4 f(x) f'(x) g(x) g'(x) | 2 4 1 3 1 2 4 2 4 1 1 3 4 h'(1) if h(x) = f(x) · g(x) f(x) h'(1) if h(x) g(x) h'(1) if h(x) = f(g(x)) 3. 2. 3.

Q: graph the function and find its average value overthe given interval. ƒ(t) = t2 - t on [-2, 1]

A: Graph of the function: f(t)=t2-t  ; [-2,1]

Q: Find the indefinite integrals (most general antiderivatives). You may need to try a solution and the...

A: Given: I=∫x3+5x-7dx we know that  ∫xndx=xn+1n+1+c                                            ..1 so,...

Q: Solve the initial value problems d2y/dx2 = 2 - 6x; y'(0) = 4, y(0) = 1

A: We have to solve the initial value problem: d2ydx2=2-6x; y'0=4,  y0=1 Integrating both sides, ∫d2ydx...

Q: 2. Find the value of k so that the function Sa² + 25 |kæ – 40 is continuous at x = 5. defined by f(x...

A: Given,          The function defined by fx=x2+25    x≤5kx-40    x>5           is continuous at x=...

Q: Use the Pythagorean Theorem to find the length of the missing side of the right triangle. Then find ...

A: In triangle ABC, using Pythagoras theorem AB2=AC2+BC2352=212+BC21225=441+BC2BC2=1225-441BC=784BC=28 ...

Q: for x 0

A: fx=x,x<0x2,x≥0 ;x∈-1,1 graph of given function on given interval can be drawn as below  

Q: Use the definition of the limit of a function of two variables to verify the limit.

A: We have to verify the limit: limx, y→1, 0x=1 According to limit value, x, y→1, 0 therefore, x=1y=0

Q: What is the principle root of √6 ? a) 3 b) 6 c) 36 d) 2.44948

A: We have to find principal root of 6. We know that a b=a×b if a and b are positive numbers. Thus we c...

Q: Find parametric equations for the lines in The line through P(1, 2, -1) and Q(-1, 0, 1)

A:

Q: Find the parametric equation of the intersection of the planes x + y = 1 and x + z = 2.

A: Equation of plane 1 - x+y = 1        Normal vector of plane 1 = n1 = 1,1,0                  coeffici...

Q: (c) Compute the inverse Fourier transform for the function Is| 4 F(6) = { -s, 0, * -s,

A:

Q: Integration techniques Use the methods introduced evaluate the following integrals. ∫ex sin x dx

A: To evaluate the integral: I=∫exsinx dx Using Integration by parts, I=∫exsinx dxI=sinx∫exdx-∫ddxsinx∫...

Q: 5-6 - Table of Values Complete the table of values for the given function. 5. g(x) = x – 4x 6. h(x) ...

A: Part (a) Given function is gx=x2-4x

Q: Arc length Find the arc length of the following curves on the given interval. x = cos t - sin t, y =...

A: Find the arc length of the following curves on the given interval. x = cos t - sin t, y = cos t + si...

Q: Solve the radical equation. V8x +9 = x +2 Which is an extraneous solution to the radical equation? O...

A: we have to solve the radical equation  8x+9=x+2

Q: 5) Find the average value of ƒ (x) = 9 – x² on [-3,3]

A:

Q: There are 25 prime numbers less than 100. The Prime Number Theorem states that the number of primes ...

A: Given, Px≈x/lnx     ......(1) (a) find P(1000) put x=1000 in equation 1 P1000≈1000/ln1000or,p1000≈10...

Q: Improper integrals Evaluate the following integrals or stat that they diverge.

A: Given:∫0∞ e-2x dx

Q: The figure shows the graph of f(x) = ex. Use transformations of this graph to graph the function h(x...

A: Graph of a function: At first we will draw f(x)=exThen we will draw f(x)=ex-1+2. The graph of the fu...

Q: Find parametrizations for the line segments joining the points. Draw coordinate axes and sketch each...

A:

Q: Show that the linearization of f(x) = (1+ x)k at x=0 is L(x) = 1+ kx. Iffis differentiable x =a at t...

A: Given:          f(x)=1+xk  at x=0.

Q: Use the graph of y = f (x) to match the function with its graph. y = −f(x − 4)

A: The function is given as y=fx. From the transformations,  y=fx→y=-fx Here , the given function is re...

Q: In real-number multiplication, if uy1 = uy2 and u ≠ 0, we can cancel the u and conclude that y1 = y2...

A: Assume that u·v1=u·v2 with u≠0. This implies that,  

Q: If f is the (constant) focal length of a convex lens and an object is placed at a distance p from th...

A: In the question, we were given the formula related to the length of the convex lens. Its equation is...

Q: A plane approaches a runway at 150 miles per hour at an angle of 8° with the runway.A vector is desc...

A:

Q: You have 1200 feet of fencing to enclose a rectangular region and subdivide it into three smaller re...

A: Let  x and y be length and breadth of rectangular region respectively. Given data, Perimeter of fenc...

Q: Center of mass of constant-density solids Find the center of mass of the following solid, assuming a...

A: Concept:   The calculus helps in understanding the changes between values that are related by a func...

Q: Find dx 2 using implicit differentiation: In x + In y + e tan x = 0

A:

Q: Evaluate the following integrals using theFundamental Theorem of Calculus.

A: To evaluate the integral using Fundamental Theorem of Calculus I=∫1311+x2dx

Q: Solve the following system dx -4x + 2y dt dy = -x - y dt

A:

Q: Solve  y"-8y'+12y= 0

A: We can solve by the finding auxiliary equation.

Q: The scalar component of H parallel to the line y=1, z=2 where H = -2a, + 3as- 4a, at p (1,90, 2) -3 ...

A: Given: H=-2aρ+3aϕ-4az p=1,90,2

Q: ntegrate using trigonometric substitution: dx 25+x2

A: It is in the standard formula  form of integration

Q: Solve the linear equation: 3x/5 - (x - 3)/2 = (x+2)/3

A: the given linear equation is: 3x5-x-32=x+23 we have to solve the given linear equation

Q: Determine whether the relation {(1, 6), (1, 7), (1, 8)} is a function. Give the domain and range for...

A: Determine whether the relation {(1, 6), (1, 7), (1, 8)} is a function. Give the domain and range for...

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.