Assume that f is a one-to-one function. (a) If f(6) = 12, what is f-¹(12)? (b) If f¹(1) = 8, what is f(8)?

Q: 4. Consider the plane : x + 3y - 2z = 6 and the line with parametric equations l: x=4-3t, y=2+t, z =…

A:

Q: iven R'(t) = (4e²t, 2t ,2cosh t), and R(0) = (1, −2, 3), 1+t² find Ŕ(t), and give the parametric…

A:

Q: ydx-xdy + xydy = 0

A: To solve the given ordinary differential equation problem.

Q: In the quadratic equation Ax2+BX+C =0, describe the roots when B2-4AC is positive. The roots are…

A: The given quadratic equation is Ax2+Bx+C=0

Q: N|- x² Given: quadric surface S with equation (y - 3)2 - 2 (a) Determine and identify the traces of…

A: Quadratic surface S with equation y-32-x22-z22=1

Q: a.) Solve the equation z³ − 1 = 0 15 1 √3 b.) Evaluate (-+-+3) " 2 2

A:

Q: · ƒ³3(x + 1)(x + 2)²(x² −1)dx with and without the even-odd theorems (show both solutions).

A: Solution :Without odd-even…

Q: Find the slope of the tangent line to the graphof the polar equation 1 r = at Ø= 1-sinø 6

A:

Q: Solve • ƒ²₂(x + 1)(x + 2)²(x² - 1)dx with and without the even-odd theorems (show both solutions).

A:

Q: (b) The function y(x) satisfies the inhomogeneous second order linear differential equation d²y dy +…

A: We have to find the general solution of the given differential equation using variation of…

Q: y = (x² + x + 1)²

A:

Q: Let S be the surface with equation (z - 4)² = 4x² + 4y². Viewing S as a surface of revolution, find…

A:

Q: 5. Find the derivatives (a-b) and the limit (c): (2) ± √( 1 cos (1²) dt) (0) ² (154) dt dx 1 r2+x…

A:

Q: Let C, D and E be the polar curies below: Cir=f(0) = 3-3 Cos 0 Er = g(0) = 12/250c4 D:r=3 (1.) Show…

A: Let's solve part 3 and 4.

Q: x² - 25 to fill in the table: Xx - 5 6 5.5 5.1 5.01 Based on ONLY the table of values above, what…

A:

Q: 1. Evaluate the integrals (a) fxsin 2xdx, (b) f(3x - 1) eª dx, Hint: Use the Integration by Parts. 3…

A: SOLUTION-

Q: Let The coefficient of x' in the Maclaurin series for f(x) is: Answer f(x)=9e2x-x.

A:

Q: Find the set of symmetric and parametric equations of the line passing through the point P(3, 4, 1)…

A:

Q: x-5 X-3+x-3' 31. Determine the lim A. 0 B. -00 C. +∞ D. does not exist

A:

Q: A rectangular field having an area of 2500m2 is to be enclosed by a fence, and two additional fence…

A: Area=L×W=2500 m2 So,L=2500W The perimeter P=2L+2W+2W {to divide the field into three 2 fences of W…

Q: 1. If x=27-3k and y = i +5j -4k, express each of the following in terms of i, j, k b) 2(3x+y)-3(4y…

A: Given x→=2i→-3k→ & y→=i→+5j→-4k→To write expression in terms of i→,j→,k→:

Q: 3. Find a vector equation of the line that.... a) passes through (-3,5,-2) and (7,-3,1) 2+6 c) is…

A: Since you have posted a question with multiple sub-parts, as per the company guidelines we will…

Q: 11. Evaluate 1 (a) √x (x² +1)³dx, (b) fdx (c) fda (d) fx x+2 ev dx √x²+4x IT'

A:

Q: A certain family in Sitio Calculus opened a t-shirt business last year. The family started with 50…

A: Given: fx=x2-2x+3 Since, the marginal cost function is the derivative of the total cost function,…

Q: 4. Evaluate the line integral along the path C given by x = 2t, y = 10t, where 0 ≤ t ≤ 1. (a)…

A: Both integral is solved.

Q: Find the general solution of the ff.differential equations.1.)dy/dx=x+1/2(y+3) 2.)dy/dx=y^2(1+e^x)

A:

Q: Evaluate the following integrals. 13 1 sin²x -dx

A:

Q: Given x - ³²+2y — In(y + 1), find the arc length for 0 ≤ y ≤4 8

A: The arc length of the curve x=f(y) for a≤y≤b is given by ∫ab1+dxdy2 dy

Q: Find the Area of the Surface obtained by rotating the curve about the x - axis y = cosh x, 0 ≤ x ≤ 1

A:

Q: d dx sinh(Vx)=

A:

Q: 3 S ₁² √ (²√₁² - ²√+²) ³ dt

A: Given

Q: ind g'(3) given that f(3) = -1 and f'(3) = 5. (a) g(x) = 2r³-7xf(x)

A: Topic:- application of derivatives

Q: Find a set of parametric equations for the curve of intersection of the paraboloid z² +4y² -z = 0…

A: Here, to find the parametric equation of the paraboloid x2+4y2-z=0 and the plane 2x-z=0

Q: 2. z = x + 2 У Х x

A: Solution

Q: 2 is: The slope of the tangent line to the curve y = - at the point 3, x The equation of this…

A: We have to find out the slope

Q: If z is a function of x and y implicitly defined by əz əz find and əx ду at (x, y, z) = (0, 2, -1).…

A:

Q: Let line 1: x = = = and point P(1,0,1). 2 ● Find the set of parametric equations of the line…

A:

Q: Find the Area of the Surface obtained by rotating the curve about the x - axis y = cosh x, 0≤x≤1

A: Area  of surface is obtained.

Q: Text Canada's population is about 33 million people. It is increasing at about 1.8% per year. How…

A:

Q: Find a particular solution of as =10csc² 2t determined by s= 2 when t == . dt

A: dsdt=10csc2(2t)  s(π/4)=2 ds=10csc2(2t)  take integration both side

Q: 1. Evaluate the line integral of E = xax - y ay along the segment P₁ to P2 of the circular path as…

A:

Q: The limit below represents the slope of a curve y = f(x) at the point (a,f(a)). Determine the…

A:

Q: 2. Consider the circle C₁ : r = 1 and the roses C₂: r= cos 20 and C3 : r = 2 cos 20, each of which…

A:

Q: to determine the instantaneous rate of change c Use f(x+0.0001)-f(x) 0.0001 f(x) = 5x² - 7x ata = 2,…

A:

Q: 2. Which of the following statements is TRUE? (Circle ALL that apply) a. |ū - v is always less than…

A: We need to check whether the given statements are true. We will check one by one.

Q: 26 Find the value of k so that line 4, 2]-[2-20]++ [2, k₁-3) is parallel to the Plane *x+24-42=12

A:

Q: Find the area bounded by the parabolas (x - 1)² = 4ay and y² + 4a = 4ax.

A: Here we have to find out the area between the given curve that is we have given two parabolas

Q: Find the volume of the solid generated by revolving the region bounded by the given lines and curves…

A: Find the volume of the solid generated by revolving the region bounded by the given lines and curves…

Q: Let C be a curve with the parametric equations à = − ln(t + 1); y = sint, t = [0, 1]. a. Set-up the…

A:

Q: Newton's Law of Cooling a) A cup of coffee has temperature 95° C and takes 30 minutes to cool to 61°…

A: SOLUTION-