(a) Evaluate the following integrals using appropriate rules: 2) ſī 2x + 3 dx (x² + 3x)'

Q: For the given function ƒ and initial approximation x0 , use Newton’s method to approximate a root of...

A:  Given function is f(x)=sinx+x-1 and x0=0.5

Q: When an equation is said to be nonhomogeneous ?

A: For a linear system of equation say - Ax = bThe equation is called homogeneous if b=0.The equation i...

Q: Find the product:: (3x + 5y)(3x - 5y).

A: We have to find the product:: (3x + 5y)(3x - 5y).  

Q: Find the sum of AB and CD, where A = (1,-1), B = (2,0), C = (-1,3), and D = (-2,2)

A: Given data: The first point given is A=(1,-1). The second point given is B=(2,0). The third point gi...

Q: For a long-distance phone call, a hotel charges $9.99 for the first minute and $0.79 for each additi...

A: Phone call rate for first minute charged by hotel = $9.99 Phone call rate for each additional minute...

Q: d²y Find- when t = 1 if given the parametric functions as below, dx2 x = 3e5t y = te-5t

A:

Q: Find the length of the curve over the given interval. r = 2a cos θ, [−π /4, π/4]

A: Since, we have to find the length of the curve over the given intervalr=2a cosθ over the interval -π...

Q: Among all pairs of numbers whose difference is 14, find a pair whose product is as small as possible...

A: We have to find a pair whose product is as small as possible where difference of pair of numbers is ...

Q: Estimate the limit numerically to two decimal places or state that the limit does not exist.

A: Given that limx→23x-95x-25. Compute the function values near 2 and table them as shown below.

Q: The resistance R produced by wiring resistors of R1 Ω and R2 Ω in parallel can be calculated from th...

A: This should be in series not parallel  The equivalent resistance R = R1 + R2 R1 = 20 ohm R2 = 30 ohm...

Q: 39. 2

A: according to given figure given function is decreasing in it's domain

Q: Find f(-x) - f(x) for the given function f. Then simplify the expression: f(x) = x3 + x - 5.

A: Given function,  f(x) = x3 + x - 5 To find f(-x) - f(x) 

Q: Assume f (x) = 6 / x. What is the slope of the line tangent to f when x = −2?

A: Given: fx=y=6x; x=-2 we know that slopem of tangent at pointx=-2 is given by m=dydx|x=-2            ...

Q: Find the limits

A: Consider the given limit, limn→∞1n+1+1n+2+⋯+12n now write the limit in the summation form, limn→∞1n+...

Q: In Exercises 36-41, use the Root Test to determine convergence or divergence ( or state that the tes...

A: Given- ∑k=0∞k3k+1k To use- The Root Test to determine convergence or divergence.  

Q: Solve the inequality using a graphing utility : x3 + x2 - 4x - 4 > 0

A: we have to solve the inequality using a graphing utility : x3 + x2 - 4x - 4 > 0

Q: Graph the linear equation: x = -3.

A: we have to graph the linear equation x=-3 the given equation can be written as: x+0y=-3x+0y+3=0 ther...

Q: Graph of a linear function Find and graph the linear function that passes through the points 12, -32...

A: Equation of a line passes through x1, y1 and x2, y2 is y-y1=mx-x1Where slope m=y2-y1x2-x1

Q: A 120-m long fence is to be cut into pieces to make three enclosures,each of which is square. How sh...

A: 120-m long fence is cut into three squares.Let the side of each square = xPerimeter of one square = ...

Q: Suppose f(x) = x2 + 1  and g(x) = x + 1    Then (f + g)(x) = (f - g)(x) = (f/g)(x) = (f ∘ g)(x) = (...

A:

Q: Factor completely. 6x4 + 35x2 - 6

A: Given expression, 6x4+35x2-6

Q: Find the values of ∂z/∂x and ∂z/∂y at the points 1/x+ 1/y+ 1/z- 1 = 0, (2, 3, 6)

A: Given equation -1x+1y+1z-1 = 0Simplifying it for z - 1z = 1-1x-1y1z = xy-y-xxyz = xyxy-y-x          ...

Q: Fill in the blank/s: If the center of an ellipse is (3, -2), the major axis is horizontal and parall...

A: Given,  Center of ellipse = (3, -2)  Major axis is horizontal and parallel to x - axis.  The distanc...

Q: A billboard, 54 feet wide, is prependicular to a staright road and is 18 feet from the nearest point...

A:

Q: Evaluate the indefinite integral. Snip    ∫ x (2x + 5) 8 dx

A: Integration: ∫x(2x+5)8dx Let, 2x+5=z Differentiating both sides we get2dx=dzdx=dz2

Q: State true or false  0 > -13

A: Given:0>-13

Q: Graph the function h(x) = (1/3)x by making a table of coordinates. If applicable, use a graphing uti...

A: Solution:-  The given function is  h(x)=13x

Q: Find the volume of the described solid S A pyramid with height  h and base an equilateral trianglewi...

A: To find the volume of the pyramid with height h and base an equilateral triangle with side a

Q: 20.Consider the equation ay″ + by′ + cy = d, where a, b, c, and d are constants. a.Find all equilibr...

A: Given                                                 ay''+by'+cy=d (a) the equilibrium solutions ar...

Q: 9. Using graph discuss continuity f(x) = *,1, -1sx< z 0 <x<1 2x,

A:

Q: The  tax table can be modeled by a piecewise function,where x represents the taxable income of a sin...

A: Consider the tax owed function T(x), here x is the taxable income. Find T(50,000). Since T(x)=4750+0...

Q: Express h(x) = (2x + 3)7 as a composition of two functions f and g so that h(x) = (f ∘ g)(x).

A: The given function is hx=2x+37. Let gx=2x+3. This gives hx=gx7.

Q: The parallelogram shown here has vertices at A(2, -1, 4),B(1, 0, -1), C(1, 2, 3), and D. Find the co...

A: The parallelogram has vertices at    and D. (a) The parametric equations of line BA is,

Q: Find the limit. Use l’Hospital’s Rule where appropriate.If there is a more elementary method, consid...

A: Let the given limit be y - y = limt→1 t8-1t5-1Using L'Hospitals rule - Differentiating numerator and...

Q: 3 Is x + 2 a factor of a* + 3a* - Зх — 10? Select an answer O The remainder when you divide is Is 2x...

A: 1) Check whether  x+2 is a factor of the polynomial by dividing x3+3x2-3x-10 by x+2. For that use th...