Question 1. Let f(x) = (x³ + x² + 1)e ³+1 and g(x) = ex³+1¸ (a) Draw a rough sketch of the graphs of the functions y = f(x), y = g(x) and the region bounded between y = f(x), y = g(x) and vertical lines x = 0 and x = 1. You can use any online graphing tools you want. (b) Find the area of the region bounded between y = f(x), y = g(x) and vertical lines x = 0 and x = 1/2. Explain your steps.

Q: If cot (x) sin (2x) = 18 (in Quadrant-I), find (Please enter answer accurate to 4 decimal places.)

A:

Q: P Given the demand equation x + 3 number of units, determine the value of p where the elasticity of…

A:

Q: 7 Suppose f(x)dx=3, f(x) dx = -5, and g(x)dx=7. Evaluate the integrals in parts a - d. >ff(x)dx=3.…

A:

Q: Calculate the gradient of this curve at the point where D = 0.25. b) Calculate the discharge which…

A:

Q: x (e) / Int √x dx

A:

Q: Does this infinite series converge absolutely, converge conditionally or diverge? Σ=z(−1)n+1 1 n(in…

A:

Q: Evaluate y³da — a³dy, where C' is the boundary of the region between the circles x² + y² = 9 and x²…

A: To find  , where C is boundary of the region between the circles

Q: series. 36 + 12 + 4 + find the sum of the infinite geometric 4 4 + + 3 9 -810 + 540-360+240-160+...

A:

Q: The daily cost (in dollars) of producing Samsung VR headsets is given by where a denotes the number…

A: we have given

Q: 4. a) Show all steps to convert the parametric curve form: x= 12-t², y = 2t. b) Identify the form of…

A:

Q: 19.fe-2x sinh² 3x dx = =

A: To evaluate the following integral.

Q: कर +0 ←← x lim (tanx)

A: we have given limit

Q: Find a unit vector in the direction in which ƒ(x,y) = √x² + y² increases most rapidly at P(π/6,π/4);…

A:

Q: Suppose F(x, y) = (2x – 2y, 6xy) and C is the line segment starting at (3, 0) and ending at (5, —4).…

A: The line segment C is defined by its two end-points:(3, 0)(5, -4)The equation of the line segment…

Q: Change the point (2√3,6,–4) from rectangular to spherical. T2 (a) 2-,- 3 3 T 2π (b) 8- 3 3 л 5л 33…

A:

Q: Evaluate the indefinite integral: Su ² (G√0 + √√ ) du

A:

Q: Find the area of the shaded regions. 16 Ay 12 8 -4 -1 (0,0) |_y=x³-4x (3,15) A o 33 O.A. 4 41 OB. 4…

A:

Q: Consider the function f(x) = 2sin(x²) on the interval 0 ≤ x ≤ 3. (a) Find the exact value in the…

A:

Q: Use a triple integral to find the volume of the solid enclosed between the cylinder x² + y² = 9 and…

A:

Q: 1 2 n(Inn)2 (f) Σ

A:

Q: The functions f and g are integrable and f(x)dx= -5, 4 [ f(x)dx= 4 (Simplify your answer.) 2 a. b.…

A: The functions  and  are integrable and .To evaluate the following.Note: Since the student has posted…

Q: Q9.7 Look at the directional fields of phase planes below. Draw a line to match each phase plane t…

A:

Q: Let F(x, y, z)=(-xz²,-4xyz, 8xy³z) be a vector field and f(x, y, z) = x³y²z. vf=(000) VXF=( Fx Vf=(…

A:

Q: Find the area of the region bounded by on the interval [1,8] f(x) = e4x and g(x) = 2x 2x on

A: The area of the region bounded by the curves y= f(x)  and y=g(x) on [a,b) is given by

Q: Convert the rectangular equation x² - xy + y² = 3 to the polar coordinates 3 2-sin 0 Or= o po² = =…

A:

Q: The Cartesian coordinates of a point are given. (a) (6, -6) (i) Find polar coordinates (r, 0) of the…

A: a) given cartesian coordinates are (6, -6)"As per the rules, we are supposed to answer the first…

Q: The following relationship is know to be true for two angles A and B: cos(A) cos(B) sin(A) sin(B) =…

A:

Q: (1) € (III) Match formulas (a)-(d) with graphs (I)–(IV). (a) s₁ = 1-1/n (c) Sn = 1/n 1 Sn 1 Sn 10 10…

A:

Q: Find a power series representation for the function. f(x) = x³ tan-¹(x³) f(x) = 8n+9(-1)" 2n + 1 Σ(…

A:

Q: r∞ 1 + x x3 J (F) dx

A: The given integral .The aim is to calculate the integral value.

Q: Find the absolute maximum and minimum values of the following function on the given interval. Then…

A:

Q: Given that f(x) dx = 3 and ſå f(x)dx = 4. 2 6 A) f f(x) dx = 2 B) f²2² 3 f(x) dx = 6 c) f f(x) dx =

A:

Q: (sin-¹ (-)) Evaluate cos (sin s

A:

Q: 6tanx- COSX 2 - 3 sin x

A:

Q: 3.) When traveling in London, Patricia decided to check her e-mail at an internet café. There was a…

A: Let fixed cost denotes by F Let variable cost denotes by V Let time denotes by t in minutes  Let…

Q: □ 1. Select the Cartesian form of the parametric curve defined by x = 6 cost, y = 6 sint. - 3² 1 6 6…

A:

Q: Find the area of the region that is bounded by the given curve and lies in the specified sector.…

A: The area of the region bounded by the curve r = f(), a ≤  is given by

Q: solution to the Second Order = 3. The general differential equation By" - ay' is in the form y(x) =…

A: The general solution to the Second-order differential equation 3y′′=2y′ is in the form…

Q: Find y'. y= (6 + X 4

A:

Q: 10. Evaluate the following limits (Aşağıdaki limitleri değerlendiriniz): x² - y² ii) lim (x,y)+(0,0)…

A: We have to find limits of the following

Q: all solutions are wrong can you please check .thanks

A:

Q: Evaluate xy'dx + x³dy, where C is the rectangle 5 C with vertices (0,0), (5,0), (5,1), and (0,1)

A:

Q: Find the area bounded by the given curves 1.) xy = 1, y = x, x = 2 and y y = 0

A:

Q: (a) Use differentiation to find a power series representation for 1 (3 + x)²· Σ((-1) "3" (n+1)x²¹…

A:

Q: 7 For the function f(x) = x³ + 3x² find the following (Show your work) (a) Intervals of…

A:

Q: Find the Cartesian coordinates of the given polar coordinates. Then plot the point. -(C (x, y) = 1.0…

A:

Q: Sketch the curve with the given polar equation by first sketching the graph of r as a function of in…

A: Given the polar equationr=θ

Q: U.S. Online Video Viewers The number of online video viewers in the United States was growing at the…

A: The number of online video viewers in the United States was growing at the rate ofr(t)=9.045e0.067t…

Q: Find the directional derivative of f at the given point in the direction indicated by the angle 9.…

A:

Q: Find the Taylor polynomial T3(x) for the function f centered at the number a. f(x) = xe-5x, a = 0…

A: