3) Let f'be the function given by (x-1)(x²-4). For what positive values of a is f continuous for all real numbers x? 2 x-a (A) none (B) 1 only (C) 2 only (D) 4 only (E) 1 and 4 only

Q: Use a table of values to estimate the value of the limit. If you have a graphing device, use it to…

A: The given limit .The aim is to find the limit using the table of values.

Q: If a = i +9j+k and b = i +19j+ k, find a unit vector with positive first coordinate orthogonal to…

A:

Q: Find the tangential and normal components of the acceleration vector. r(t) = (3t – t³) i + 3t² j O…

A: Take derivative.Find the magnitude.

Q: Find the equation for the plane through the point P = (0,4, − 1) and normal to the vector n = 2i-7j…

A:

Q: -8 g(x) -6 -5 5 U -1 3 0 2 1 3 5 5 00 8 6

A: x-8-5-10158g(x)-6532356

Q: Solve the initial-value problem d²y dt² dy dt +14- +49y0, y(1) = 0, dy (1) = 1.

A:

Q: The temperature in degrees Celsius on the surface of a metal plate is given by T(x, y), where x and…

A: The temperature in degrees Celsius on the surface of a metal plate is given by T(x,y), where x and y…

Q: There is a horizontal line (of the form y = b) that divides the region bounded by the curves y = x²…

A:

Q: (a) Complete the tables for the given values of ___. Round to the nearest tenth as needed. (b) Graph…

A: given polar equation

Q: The parametric equations below describe the line segment that joins the points P₁(X₁,Y₁) and…

A:

Q: 5. Let f: Z→ Z defined by f(x) = 4x² - 3. Determine the following. a) Domain d) Is f one-one? b)…

A: Since you asked multiple sub parts questions, according to our policy we can solve only first three…

Q: Find the average value of the function f(x) = 1 + x² on the interval [−1, 2]!

A: Given function To find: Average value of the function over the interval [-1,2]

Q: Suppose that the price and supply for a certain model of graphing calculator are related by p = S(q)…

A:

Q: Find three mutually orthogonal unit vectors in R³ besides ±i, ±j, and ±k. There are multiple ways to…

A: Assumed vectors:The unit vectors are the vectors whose magnitude is 1.Assumed vector u is not an…

Q: 1. Calculate the difference quotient, simplify your final answer. f(x+h)-f(x) h for the function f…

A: Answer is in step 2.

Q: (e) Sex ex cos x dx x³ In x dx (d) (f) [x sec² x dx

A:

Q: In this question you will work out the first few terms in a Taylor series. Suppose that we represent…

A: The given function The Taylor series

Q: 8. For a real number c, let f(x) (b) Calculate lim f(x). *-*+ (a) Calculate lim f(x) as an…

A:

Q: Simplify sinh (4 In (3x)).

A: To simplify the expression sinh⁡(4ln⁡(3x)),We can use the properties of hyperbolic trigonometric…

Q: ns Now suppose O If we knew what the graph of f looked like, then we could read off from that graph…

A:

Q: Determine the intervals of continuity for the given function. At which endpoints of these intervals…

A: Solution is following in explanation step.

Q: In Problems 13 and 14, determine by inspection at least one solution of the given differential…

A:

Q: u = cos 0 i + sin 0 j cuando (a) 0 = 00 y

A:

Q: Evaluate the limit analytically (without tables or graphs), using techniques that have been shown to…

A:

Q: Given a function h(x) = x-2 Sgn (x) where sgn(x) called - signum function is defined as sgn(x) =…

A: Given a function  where  called signum function is defined as To evaluate the following:

Q: Find the gradient of the function at the given point. f(x, y) = 3x + 4y² + 2, (3, 1) Vf(3, 1) = = X

A:

Q: If f and g are the functions whose graphs are shown, let u(x) = f(g(x)), v(x) = g(f(x)), and w(x) =…

A: Given that:-

Q: Find the standard parametrization for the line segment joining the points below. Draw coordinate…

A: Solution is following in explanation step.

Q: Suppose the profit from the sale of a items of a product is P(x)= = -x² +112x 1711. What two…

A: The Profit from the sales of x items of a product is

Q: Find the gradient of the function at the given point. Function f(x, y, z)=√√√√x² + y² + z² Vf(7, 3,…

A:

Q: Let f(x)=√x + 10x Find the slope of the secant line on the graph of f(x) for each interval: [16,…

A: The given function is The slope of secant line passing through points

Q: If lim 1-0 x² ** a. lim f (x) -O b. lim x-0 5, find the following limits.

A:

Q: 1. Find the parametric equations for the line through (1.4,0) and perpendicular to both i+j and j+k.…

A:

Q: use implicit differentiation if applicable show proof (complete solution) y=e(x+c) is a solution of…

A: The given equation is

Q: The length of a rectangle is 41+5 and its height is t, where t is time in seconds and the dimensions…

A: Area of the Rectangle is given as Where l is the length of the rectangle b is the width of the…

Q: Differentiate y = In(x³ + 2). Solution To use the Chain Rule, we let u = x³ + 2. Then y = In(u), so…

A:

Q: According to one cosmological theory, there were equal amounts of the two uranium isotopes 235U and…

A:

Q: the f(x) 4 3 g(x) 6 5 4 LE 3 2 1 2 2 1 0 0 a) lim (f(x) + g(x)) X→ 1+ b) lim (f(x) + 2g(x)) X→ 1- c)…

A:

Q: 1. Sketch a graph that satisfies the given conditions: lim f(x) = 1 x-0 lim f(x) = 2 x-0 2. Sketch a…

A:

Q: Q2. Find area of the region in 2D plane (x,y) given by: (it is sufficient to provide an expression…

A:

Q: Calculate the average rate of change of the given function over the given interval. Where…

A: The given function is

Q: The approximate percentage of people, P, below the poverty level in the US is given in Table 2. (a)…

A:

Q: 1 In the following exercises, use the graph of the function y = f(x) shown here to find the values,…

A:

Q: 1. y = 1/x3/2, x = 4, the x-axis to the right of x = 4.  2. y = 1/(x + 1)3/2, the coordinate axes,…

A: (1) y=1x3/2,x=4, the x -axis to the right of x=4

Q: Newton's Law of Cooling tells us that the rate of change of the temperature of an object is…

A: Newton's Law of cooling states that rate of change of temperature of an object is proportional to…

Q: An object moving with increasing velocity at a rate of feet per second is displayed by the given…

A:

Q: Jse logarithmic differentiation to find the derivative of the function y = x+8 cos(x) 8x8

A: To find the derivative of the function using logarithmic differentiation

Q: Video Example Find the critical numbers of the function. f(x) = x³/5(7 - x) Solution First note that…

A:

Q: Determine the symmetries (if any) of the graph of the given relation. 5y = 4x² - 7 *** Choose the…

A: Check symmetry of graph

Q: (1) [xe5x-2 dx (h) [ cos x In (sin x) dx

A: