31. The function fƒ: R→ R is defined by f(x) = (a) Show that f is a bijection. (b) Determine f¹(x) x 1 1 -1 ,if x < 1 if x > 1.

Q: V.P. [ -8 COS X (a²-x²) -dx, (a> 0).

A:

Q: 21

A:

Q: Find the regions where sinx sx.1

A: Topic:- trigonometry

Q: R is the region bounded above by the graph of f(x) = 4x - 2x² and below by the x-axis. Find the…

A:

Q: 3. Evaluate 622 dV where G is bounded by r+ 2y + 4z = 8 in the first octant.

A:

Q: Let F(x) = f(f(x)) and G(x) = (F(x))². You also know that f(9) = 7, f(7) = 3, f'(7) = 8, f'(9) =…

A:

Q: Differentiate f(N) = (N) = 0 bN² + N with respect to N. Assume that b and K are positive constants.…

A:

Q: Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of…

A:

Q: Prove that if i and k are relatively prime positive integers, for every positive integer l the…

A: Concept: Number theory: Number theory is an area of mathematics that aids in the study of the set of…

Q: Find the values of a that satisfy the inequality a. (x-1)(3x) > 0 b.2< 3x+1 2x+4

A:

Q: 18. Up to what derivative is the derivative of y = x6 + 2x5 - 4x4 + 7x³ becomes 0.? a. yv b. yu c.…

A:

Q: Find f(t). ℒ−1{9s / (s - 4)2}

A:

Q: Describe the advantages and disadvantages of using linear scale axes versus logarithmic scale axes…

A:

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) t²3t- 28 lim t→7 t-7

A:

Q: Let R be the region bounded by the following curves. Find the volume of the solid generated when R…

A:

Q: Consider the utility of a consumer consuming two goods, the quantities of which are x and y. His…

A: To find out the levels of x and y which will maximizes the utility.

Q: Find the area moment of inertia with respect to x of the plane region y=9-x^2 bounded by the…

A:

Q: Consider the function F, that assigns x in its domain to x² - 1 F(x) = |x-1| In its domain. a. What…

A:

Q: Use the shell method to find the volume of the solid formed when a hole of radius 1 is drilled…

A: We have to solve above problem.

Q: Question 1 If A = sin ui + cos uj + uk, B = cos ui - sin uj - 3k, and C = 2i + 3j - k, find (A X…

A:

Q: 2x² + y² +3z² = 1 y² = 4x x² -z² = y 2z = x² +4y² 2x + y − z =1 z = 4y²-x² E

A: We have to match the graph with equation and write name of these shapes.

Q: Find the regions where sinx sx.1

A:

Q: • III.6 622 dV where G is bounded by r + 2y +4:= 8 in the first octant. 3. Evaluate

A:

Q: Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of…

A:

Q: Find  f(t). ℒ−1{1/(s - 7)3}

A: The inverse laplace tranform L-11s-73

Q: 2 1. f(x) = x² + 8x + 12 2 2. f(x) = x² + 25x 150 3. f(x) = x² + 18x130

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Decreasing Annuities The second account earned interest for two months, so if the initial balance…

A:

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) lim X-6 - (8 - 1—² x )…

A:

Q: Example 12: Sketch a graph of the function f(x) = x¹ = 4x³ + 10 using the following steps. 32 (a)…

A:

Q: Find the regions where sinx sx.1

A:

Q: Find the tangent line to f(x) = ax³ at x = -1. Assume that a is a positive constant. ***

A:

Q: Prove or disprove that the series below converges n-1 Σ(-) n=1

A: Let's prove that given series is converges or not.

Q: s shown in the required reading or videos ove that the harmonic series below diverges ithout using…

A:

Q: Find the derivative of the following exponential and trigonometric functions: please attach your…

A:

Q: Deriving the formula for volume generated by revolving the first- = quadrant area bounded by the…

A:

Q: 2 z² +4 lim z 2i 2z²+(3-4i)z-6i

A:

Q: Use the Laplace transform to solve the given initial-value problem. y'' + 2y' + y = 0,  y(0) = 1,…

A: A detailed solution is given below.

Q: The midpoint of AB is at (0, 0). If A = (-5, 4), find B. B is: (

A: Given :A=-5, 4Mid Point of AB=0,0

Q: Betermine the value of k for which the following planes are perpendicular: π₁ = (1, 2,7) + s(4,2,0)…

A: π1 = (1,2,7)+s(4,2,0)+t(k,1,2)  First need to find the normal of the planeIf the plane in the form…

Q: Prove lim x-a 4x 4a, using the ɛ, 8 definitions of limit.

A: The given limit,   limx→a4x=4a

Q: 18. The solution of the differential equation 2xy = x² + 3y² when y(1) = 3 is dx

A:

Q: Given f(x,y)=x²y³-4y, find the directional derivative at the point (2,-1) in the direction of v=.

A:

Q: 9- a) Evaluate the following integral. b) Find the indefinite integral: S S₁² 5Cos(t) 3.Sin5 (t)…

A:

Q: iii please, NOT i or ii

A: Topic:- vector algebra

Q: 2. Consider the function F, that assigns x in its domain to x² - 1 F(x) = |x-1| In its domain. a.…

A:

Q: Find the normal line to f(x) = ax² - 4ax at x = 3. Assume that a is a positive constant. Next…

A:

Q: Find the constant a such that the function is continuous on the entire real line. f(x) = √5x², x ≥ 1…

A: We need to find a.

Q: Given: y = x - sin(2x) Find: dy dx 0 - cos²x 2 ○ - sin² x 01+ cos²x O sin²2 X

A:

Q: 3 E (It=X) xp x te

A:

Q: Given: y² = 2x - 2 bounded by y = x-5. The points of intersection of these two curves are {A}…

A: y2=2x-2 bounded by y=x-5