(h) Write the number in the form a + bi. 1 i. ef ii, ef

Q: If f(x) = x2 and g(x) = x + 2, find (f ∘ g)(x) and (g ∘ f)(x).

A: Find f∘gx as shown below: f∘gx=fgx              =fx+2              =x+22              =x2+4x+4

Q: Solve absolute value inequality : lx - 1l ≤ 2

A:

Q: Find an equation of the tangent line to the graph at the given point. (x + 2)2 + (y – 3)² = 37, (-1,...

A: We have to find equation of tangent line to the graph of function: x+22+y-32=37 at -1, 9 We know equ...

Q: Calculate the first quadrant area bounded by the following curves: y=x²+2, y=4 and x=0.

A:

Q: Find the general solution to the given differential equation. (Use C for the constant of integration...

A: Given,         dydx=x5y

Q: Fill in each blank so that the resulting statement is true. √(a)2 = ...........

A: Our Aim is to fill the given blank below so that the resulting statement istrue:-(a)2 =?  -(i)

Q: Evaluate the integrals

A:

Q: find the total area between the region and thex-axis. y = -x2 - 2x, -3 ≤ x ≤ 2

A: The region and the x-axis given is y = -x2 - 2x, -3 ≤ x ≤ 2. To find the area  between the region an...

Q: y''-2y'+y=0  ADD   For e^x and xe^x  show that functions are linear independent solutions.

A: Given equation is y11-2y1+y=0 Show that the equation has linear independent solutions

Q: Find the general solution of the differential equation.

A: Given: dydx=4x+4x16-x2

Q: 73. Use Integration by Parts, with u = In x and dv = x dx.

A: By parts integration formula is as ∫udv=u∫dv-∫∫dvdu  ....1

Q: Fill in the blank/s : x/5 ÷ x/3 = ............, x ≠ 0..

A: The given expression (division) is: x5÷x3 The replace division symbol with multiplication symbol, mu...

Q: Equations of lines Find both the parametric and the vector equations of the following lines. The lin...

A: Given: The line through 0, 0, 1 in the direction of the vector v = 4, 7, 0. To find: Parametric and ...

Q: Find 0ƒ/0y as a function if ƒ(x, y) = y sin xy.

A: fx, y=ysinxy

Q: Use L’Hôpital’s Rule to determine the comparative rates of increase of the functions f (x) = xm, g(x...

A: limx→∞lnx3x=limx→∞3lnx2·1x1    By using L'Hospital's rule=limx→∞3lnx2x=limx→∞3·2lnx·1x1    By using ...

Q: Evaluate the integral.

A:

Q: Solve the equation or inequality: sin θ cos θ = - 1/2, 0 ≤ θ < 2π.

A: Consider the equation: sinθ·cosθ=-12,   0≤θ≤2π

Q: The average weight, W, in pounds of an adult is a function, w = f(c), of the average number of calor...

A: (a) f(1800)=155this implies calories is 1800 and weight is 155.so, the average weight 155, in pounds...

Q: Q5,Q6

A: A Maclaurin series is given by f(x) = ∑k=0∞fk(0)k !xk Given function f(x) = x5 tan x     Here, each...

Q: Explore the convergence of the series:

A:

Q: Verify the identity: cot(-x) sin x = -cos x

A: cot(-x)=-cot(x)cot(x)=cos(x)sin(x)

Q: Solve, a. Find the slant asymptote of the graph of the rational function f(x) = (x2 +4)/x. b. Follow...

A: We have given rational function fx=x2+4x a.   x2+4=x.x+4 Therefore, slant asymptotes is y=x. b. Step...

Q: dx

A:

Q: 2. Consider the graph of the functions f, and g (below). yA 1 1 a) Which is larger, f(6) or g(6)? b)...

A: Given that, The graphs of function f and g as follows:  

Q: Find the general solution to the given differential equation. (Use C for the constant of integration...

A: Given differential equation dydx=x2+xy+9 We have to find the general solution of the given different...

Q: In Exercises 10-37, evaluate the indefinite integral. Remember, there areno Product, Quotient, or Ch...

A: ∫xx2-4 dx Put, x2-4=t⇒2x-0=dtdx⇒2x dx=dt⇒x dx=dt2

Q: Find the area between the curve y = 2(ln x)/x and the x-axisfrom x = 1 to x = e.

A: Consider the given: y=2lnxxandy=0Interval 1,eFind the area:A=∫1e2lnxx-0dxA=∫1e2lnxxdx

Q: Find the absolute maximum and absolute minimum values of fon the given interval. f(x) = [0, 3] x +1 ...

A: Given function - f(x) = xx2-x+1Let's first find the critical point at f'(x)=0,Differentiating f(x) w...

Q: True or false: A function can have more than one y-intercept.________

A:     The statement is:  A function can have more than one y- intercept._________    

Q: Graph the polynomial function: f(x) = 2x2(x - 1)3(x + 2)

A: The polynomial function f (x) = 2x2 ( x - 1)3( x+ 2).  

Q: Use a graphing utility to graph the function y = cot(x/2).Use a viewing rectangle that shows the gra...

A: y=cotx2

Q: Evaluate the given integral by changing to polar coordinates. || cos V x2 + y2) dA, where D is the d...

A: To evaluate the integral by using the given function. The given integral function is ∫∫D cos x2+y2  ...

Q: In Exercises 45–74, compute the derivative using derivative rules that have been introduced so far.

A: Given, y=4e-x+7e-2x Now differentiate the above equation with respect to x we get, dydx=ddx4e-x+7e-2...

Q: Use the properties of logarithms to expand the logarithmic expression.      ln(xyz)

A: Given: ln xyz To expand: The given logarithmic function.

Q: A spring gun at ground level fires a golf ball atan angle of 45. The ball lands 10 m away. For the ...

A:

Q: Find the product. (x - 3y)(2x + 7y)

A: it is given that, (x - 3y)(2x + 7y) We have to find the product.