4. Find the limits (a) lim x-1 (b) lim x-0 xª+¹(ln x + 1) − x 1-x ((² + 2)1/²) 1/². e

Q: Find the value of a for which v= 8 a -4 -12 is in the set 4 0 -4 -1 0 {6E9 2 -3 5 -3 -4 2 H = Span

A:

Q: (a) (c)= dx (c) & √(x²). (e) d [ƒ(g(x))]= (g) (sin x)= dx (i) --(tan x) = dx d (k) (sec x) = dx (m)…

A:

Q: dy' dx (6.) (i + cos x ) = X = 0 y = 1 sinx (sinx tsinxcosx -y) Answer: C=1/12/2

A:

Q: g(x) = (5+3x)/(x−3) (a) What is the domain of g(x)? (b) Verify (with a sketch and/or short argument)…

A: The given function is

Q: Differentiate. h(w) (w³ + 4wª) (w 4 - w-6) = -4. −6) (5w4 + 16m³) + (w³ + 4w4 ) ( −4w−4 – 6w¯ - W…

A:

Q: 3) The twice-differentiable function fis defined for all real numbers and satisfies the following…

A: Given that f is twice differentiable function for all real numbers and satisfies the conditions

Q: Evaluate the following integral. 2 S 0 √16-x dx 2

A:

Q: Find the adjoint of the matrix A. Then use the adjoint to find the inverse of A (if possible). (If…

A:

Q: Let f(x) = pit -1-7x Then f'(x) = Write the equation of the tangent line to f(x) at x = 0:

A:

Q: Determine whether the equation is exact. If it is, then solve it. (cos xsin y-2x)dx + ( sin x cosy -…

A:

Q: A particle moves according to a law of motion s = f(t), t ≥ 0,  where t is measured in seconds and s…

A:

Q: Express the integrand as a sum of partial fractions and evaluate the integral. S 23dx (x²-1) ²…

A:

Q: dz дz Find the values of and at the given point. дх ду 2z³-4xy + 5yz + 2y³ - 35= 0, (3,3,1)

A:

Q: For the given position vectors r(t) compute the unit tangent vector T(t) for the given value of t.…

A: The given position vectors (A) (B) (C)

Q: find 5x² then find dy in terms of x and y. X If 3y - xy = 5x² then

A:

Q: Question 3.13) (see boxed comment above) Is the following function differentiable at x =2? [x² if…

A: The function is differentiable at x=2 if,

Q: Use the method for solving equations of the form following differential equation. dy dx 19x + y - 19…

A:

Q: Determine whether the equation is exact. If it is, then solve it. 2e¹ (3y - 4t)dt + (7 + 6e¹) dy = 0…

A: The given differential equation is 2et(3y-4t) dt+(7+6et)dy=0

Q: in millions of dollars). Determine how these four sectors would react to an increase in demand for…

A: To determine how these four sectors would react to changes in demand, we can use the concept of the…

Q: Use cylindrical coordinates to find the volume of the solid bounded by the graphs of z = 41 - x² –…

A:

Q: Let R be the region enclosed by the curves y = x 2 and y = √ x. Find the volume of the solid…

A:

Q: If y = (3x)4*, then dy dx (Be sure to express your answer in terms of x) =

A:

Q: Sketch the region whose area is given by the definite integral. Then use a geometric formula to…

A:

Q: Ex 3.7.3: Differentiate each equation. 2x a) y = e²x (2x - 7)5

A: Given Function for differentiation is given as follows Chain Rule formula is given as follows

Q: B. Given the function defined by f(x)= continuous at: i. x=1 ii. x=3 (3x-2 5x-1 2 2x-3 x23 1<x<3,…

A:

Q: S = {2x : x € T} where T = {y : 3y € W} and W = {1,3,7}.

A:

Q: Let /(x) = √ 4ï² + 5x + 5 Make sure to simplify your answer using positive fractional exponents.…

A:

Q: Find a vector orthogonal to both ⟨1,−4,0⟩ and to ⟨0,−4,2⟩ of the form ⟨1,_____ ,_____ ⟩ 9. Let…

A:

Q: I si sin³ (x) cos² (x) dx

A:

Q: derivative y = 3 2(4x-1)

A: Given that the expression to find the derivative of the given expression

Q: A sequence of four numbers begins with 2, and ends with 64: 2——64 If the sequence is arithmetic,…

A: A sequence of four numbers begins with 2, and ends with 64: 2——64If the sequence is arithmetic, then…

Q: Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the…

A: In this question, we will find the value of 'c'.

Q: a kite 50ft above the ground moves horizontally at 9ft/s; at what rate is the angle between the…

A: A kite 50ft above the ground moves horizontally at 9ft/s. To determine the rate at which the angle…

Q: Find the Maclaurin series of Σ το sin(t) -dt.

A: To find the Maclaurin series of

Q: Given y = f(u) and u = g(x), find dy dx y = tan u, u = 11x-4 = f'(g(x))g'(x) = dy -= f'(g(x))g'(x)…

A:

Q: For the function y = f(x) = 6 5+x²' a. Find the slope of the line tangent to its inverse function at…

A: Definition used -        Inverse of a function -         For finding the inverse of a given…

Q: Find the volume of the solid bounded by the graphs of x² + y² = 4, z = 4x + 5y, and the coordinate…

A:

Q: Let f(x, y) = y³-24x -3x²y. Find all local extreme points of f(x, y) and classify them.

A:

Q: Expand the quotient by partial fractions. 7x-27 x² - - 8x + 15 7x-27 x² - - 8x + 15 (Simplify your…

A:

Q: Consider the function f(x) = 2³. Which of the following functions are equal to f(x)? Select all that…

A: We have given,   f(x) = 23x

Q: a) Evaluate the following limits. Show proper steps. 8x²-2x-3 2x+1 a) lim 1 X--- 2 2x x-0 √2x+1-1 b)…

A:

Q: The total cost (in dollars) to produce q units of a good is given by the function: C(q) = 4.9q +…

A: Given, C(q)=4.9q+41000

Q: Find the average value of the function over the given interval and all values of x in the interval…

A:

Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of dy dx -0 y = - 4x cos(x)…

A:

Q: Find the Maclaurin series of 9*. Σ n=0

A:

Q: A solid ball is thrown straight upward from the ground y0 = 0 feet with initial velocity v0 =…

A: A solid ball is thrown straight upward from the ground y0 = 0 feet with initial velocity v0 =…

Q: The graph of f' (not f) is given below. At which of the marked values of x is A. f(x) greatest x =…

A:

Q: A rectangle has a length of 6 inches and a width of 5 inches whose sides are changing. The length is…

A: A rectangle has a length of 6 inches and a width of 5 inches whose sides are changing. The length is…

Q: Find the directions in which the function increases and decreases most rapidly at Po. Then find the…

A:

Q: Find the derivative of the function at Po in the direction of A. f(x,y,z) = xy + yz + zx, (1,-1,3),…

A: