For which value(s) of k, if any, is the function 1 (²) = x [kx² - log₂ (x) 2xk²x + 5 continuous on (-∞, ∞)? Show all your work. x ≥ 4 x < 4

Q: Find the volume of the solid generated by revolving the region bounded by y = 2x, y=0, x=0, and x =…

A: The given lines are y=2x, y=0, x=0 and x=4.   So, the bounded region is as shown below. Apply the…

Q: If Vf = F, then F is called a potential vector field, and f is called a conservative function. O…

A: Answer: True

Q: Find the area (in square units) bounded by the parabolas x² + 2y - 8 = 0. a. 7.10 sq. units b. 7.01…

A: Here we have to find the area bounded by the parabola.

Q: Sketch the region on the plane defined by the following integral. Then, switch the order of…

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Q: 1.) a function f f (x,y, 2) = 2-eªsing is given. of this function p= ((n 3, 31,-3) at the point what…

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Q: 1) If y = (x-a)√2ax-x² + a² sin-¹(*), then y' = 2√/2ax - x² a a is constant. 2) If f(k)= k√a²-k² +…

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Q: Express the vector v with initial point P and terminal point Q in component form. P(3, 3), Q(5, 5)

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Q: 2. A cyclist applies a force F with magnitude F = 50N in the same direction as the vector b = 4 j.…

A: We have to find the vectors.

Q: Question 10 The parametrization describes a cone. O True O False r(u, v) = (u, sin v, cos v)

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Q: Find lul, Ivl, 12ul, |2v|, lu + vl, lu − vl, and _|u| - |v|. u= 5i + j, v = 2i - 4j

A: We need to calculate the magnitudes of given vector and evaluate the given expressions.

Q: Convert the rectangular coordinates (5,-5√3) to polar form. Letr> 0and 0 <0<2TT.

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Q: 4) Use Green's Theorem to evaluate f √1+x³dx + 2xydy. C is the triangle with vertices (0,0), (1,0),…

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Q: Use double integration to find the volume of the solid on the first octant enclosed by the curves x²…

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Q: Q3) Assume A = [4 6 3 11 7 2 [32] and B = 1 14 5 show that (AB)' = B' A' 31

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Q: An 84 cm wire is cut into three pieces. The second piece is 4 cm longer than the first piece and the…

A: According to our guidelines we are supposed to answer only the first question if you want any…

Q: Find the equation of tangent line to Graph of f(x)=3 x In(5x-4) at point where x=.1

A: Solution:

Q: 3. fx²(9-x³)5 dx 4. J√4x-1 dx

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Q: Find the general solution of the following DE. xy² (y')² + y(x - 1)y' - x³ = 0

A: The given differential equation,    xy2y'2+yx4-1y'-x3=0

Q: Question 5 Given the function y = f (x) defined at all real values of x. Let x = 2, 3, 5 and 7 are…

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Q: termine the absolute maximum and minimum values of f(x) = cos²x-cosx the interval 0≤x≤ 2π.

A: Please refer to the image below

Q: Use the graph of f in the figure to do the following. a. Find the values of x in the interval (0,5)…

A: To answer the given questions using the given graph.

Q: 1. Find the Inverse Laplace Transforms of the following. 4 1) -1 S-3

A: The general formula we have that  Laplace transform of eat u(t) is 1/(s-a)

Q: For the function f(x) = 2x², make a table of slopes of secant lines and make a conjecture about the…

A: Slope= df/dx

Q: ered # tion Bi Q) choose one only 1. If (x + y)² = x² + y² prove that = - dx 2. If y = sin³ () cos³…

A: To find the differentiation of given functions.

Q: 5.) I. b -3 -6 Simplify. Write "undefined" for expressions that are undefined. S + toom 6 0

A: Answer (5) We have to simplify

Q: Find dy/dx by implicit differentiation. (cos X + sin #Y)5 = 49

A: The given equation is;  (cos pi x +sin pi y) 5=49.

Q: Find the ratio of the length of minor axis to the length of the major axis of the ellipse 9x2 + 16y2…

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Q: If a rock is thrown upward on the moon with a velocity of 15 m/s, its height (in meters) after t…

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Q: Find the area contained between the two curves y = 3x - x² and y = x + x². 1/3 sq. units 1/4 sq.…

A: Let's find area between two given curves.

Q: Find all the values of x such that the given series would converge. ∑_(n=1)^infinity((−1)^n x^n…

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Q: p and q are complex numbers such that pl = 7√2 and p+ql = 12√//3. On what interval must g fall on? O…

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Q: Consider the position function s(t)= - 16t+96t representing the position of an object moving…

A: Given problem:- Consider the position function s(t) = - 16t2 + 96t representing the position of an…

Q: Find the average value of the function on the given interval. f(x)=√x+3; [1, 22] (Type an integer or…

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Q: 13. In |z|

A: It is depend upon the property of complex number and thier Logarithmic.

Q: Evaluate the following limit, if it exists. lim (8-1/2) x→6

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Q: Find the volume of the solid generated by revolving the region bounded by the lines and curves y=√x,…

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Q: If Vf = F, then F is called a potential vector field, and f is called a conservative function. True…

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Q: Estimate the double integral_R  (3xy^(2)+2x^(2)) dA where R= [0,1] x [0,1] by diving R into four…

A: We need to evaluate integral.

Q: Eliminate the parameter t to find a simplified Cartesian equation of the form y = mx + b for fæ(t) =…

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Q: 3. [7.3] Determine the dot product between the two vectors below if there are 135° between them as…

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Q: Given f(x,y) = 6x^2 - 2x^3 + 3y^2 + 6xy. Determine any local maxima, local minima, and saddle…

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Q: dy 1. If (x + y)² = x² + y² prove that 11 I Alx y

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: Assume A = 21 2] and B = 1 3 [43] [4 3 11 7 6 show that (AB)' = B' A'

A: Given matrices A and B, To show that AB'=B'A'

Q: S₂ 10 x 4x²8x +9 in14 (x-1)² +51 + √5 tan¹ (²²) + C Option 1 In 14 (x-1)² +51 + √5 tan¹ (2x = ²2) +…

A: SOLUTION-

Q: -6 +][]+ 3 5 0 3 -2

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Q: A) Suppose that f(5)=-8, g(5)= 2, f^’(5)=10 and g^’(5)=-4, find h^’(5)=, if h(x)=[f(x)+2g(x)]^4 B)…

A: Suppose that f(5)=-8, g(5)=2, f'(5)=10, g'(5)=-4

Q: Solve the equation: (D² - 4) (D+2) y = 0 Oy=c₁e²x + c₂x²x + c3e-²x Oy=ce+exe + c3e

A: To solve the given differential equation.

Q: Q) choose one only 1) If y = (x − a)√2ax − x² + a² sin-¹(*), then y' = 2√/2ax-x² a a is constant. 2)…

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Q: C. Find the average rate of change of the given functions at the indicated interval. 1. f(x) = x² at…

A: We know that average value of function f(x) on given interval [a,b] is f(b)-f(a)b-a

Q: 7) Use the double integral of a cross product to find the surface area of x = z² + y that lies…

A: Let's find surface area  by using double integral.