B. Find the slope of the curve at the given point. 16. 2x²-3x+1 at (2, 3) 17. =3x²-2x+1 at (-1,6) 18. y=x²-3x+4 at (2, 2) 19. y = x²+2x-3 at (-2, -3) 20 y = 3x² + 4x-2 at (-1-3

Q: In spherical coordinates, the equation below describes what? O a plane O a cone O a sphere O a…

A: topic- spherical coordinate system

Q: 6.) I. Simplify. Write "undefined" for expressions that are undefined. -3 -6 -2 +69 4 -4 6

A:

Q: 1. Find the area bounded by the curve y = x^2  and the x-axis and the ordinates x = 0 and x = 2 2.…

A:

Q: 1-1 flood

A:

Q: 8x²-x+8 x(x² + 4) 2 lnx + 6 in (x²+4)-4 Arctan ¹ (1) + C Option 1 4 Inx+6 In (x²+4)- Arctan (+C…

A: topic -indefinite integral

Q: The graph of y g() is shown below. The areas trapped between the curve and the x-axis are given…

A: Here is the solution

Q: Let F be the vector field defined on the plane by F(x, y) = (x¹+3y, 6x - siny). Let C be the unit…

A:

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

A:

Q: 4. If 6.5 m³ of oil weighs 46,800 N, calculate its density in kg/m³. (a) 285 (b) 258 (c) 82 (d) 734…

A: Given problem:- 4. If 6.5 m³ of oil weighs 46,800 N, calculate its density in kg/m³. (a) 285 (b) 258…

Q: The area bounded by the parabola x²- 2x+y=3, the y axis and the line y=4 revolves about line y=4.…

A:

Q: Find the area of the region bounded by the parabola y² = 2x − 2 and the line y = x − 5. 16 17 18 19…

A: y² = 2x -2  y = x -5  Here we have to find intersection point  x = (y² +2)/2  x = y+5  Compare both…

Q: Let f(x, y) = 10-3r² +4. (a) Find the gradient Vƒ(2,-3) of f at the point P(2,−3). (b) Find the…

A:

Q: cos 3t dt 5 + 3 sin 3t Ocos 3t

A:

Q: Using the letters in the word COSINE arranged in random order, what is the probability that the…

A:

Q: If u and are non-zero vectors and Proj=0, then which one of the following must be true? O The two…

A: Two vectors u and v are orthogonal if u.v =0 .

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: Problem #1: Using lim 0 6x³ 8x 2 at x = -2, f(x+h)-f(x) h Find the slope of the tangent line y =

A: Let's find slope of the tangent line by using limit definition.

Q: II. Find the inverse of each matrix. 5 -11 1. -7 -9

A: A-1 =1AadjA .

Q: Convert the Cartesian coordinate (6,2) to polar coordinates, 0 ≤ 0 < 2π r= 2√10 Enter exact value.…

A: Given:    Coordinate : ( 6 , 2 )       0 ≤ θ &lt; 2π

Q: the polar coordinates to find the volume of a sphere of radius 1. -

A: Given;  Sphere of radius 1.

Q: Which is an equation of a line? A. y = 4 B. x = y^2 -4 C. y^2 = x^2 + 4 D. x^2 + y^2 = 0

A:

Q: 8+6.4+5.12+... Which one of the following is the sum of this infinite series? a) 40 b) 35 c)…

A: topic- geometric series

Q: Find the area contained between the two curves y = 3x - x² and y=x+x². 71/6 81/5 91/4 62/3 None of…

A:

Q: 1-√3-x 4. lim. x→2 4-x²

A:

Q: af axdy of f (x, y) = xy(x+y — 1) — x² Find-

A: The given function is: fx,y=xyx+y-1+x2   As we know that; The Power Law: ddxxn=nxn-1 The Product…

Q: Given the function y = x(x + 1)3. Determine the value of its second derivative at x = 1.

A: Given the function  y=xx+13. We have to find the value of its second derivative at x=1.

Q: 1 - cos 4x 1 + cos x dx

A: The given integral,     ∫1-cos4x1+cosxdx

Q: Let p(t) represent the population of a major city t years after 1950, as shown in the table and…

A:

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

A:

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

A:

Q: Find the indefinite integral. (16x +13) In (2x)dx Select the method of integration that should be…

A: Integration by parts ∫udv=uv-∫vdu

Q: a. y = 3et-2 et +1

A:

Q: 1. Be the data set according to the following table of values: On a coordinate plane, plot the data…

A: topic- exponential function

Q: Evaluate the double integral: To L 0 y x7 +1 y¹/3 x7 dx dy.

A: The given integral is: I=∫08∫y132yx7+1dxdy   So, The limit of the x varies from y13 to 2. The limit…

Q: Find the derivative of the function and then evaluate at the given point. y = 2x² - 3x: (-1,5)

A:

Q: Find the area of the region in the first quadrant bounded by the curve y = √x² +5, the x-axis and…

A:

Q: 2. If g(x)=√√3-x and f(x) = x³ +1 evaluate the following: gof(-1) b. (g-f)(2)

A: Given, g(x)=3-xf(x)=x3+1

Q: (EQUATION

A:

Q: x² +9 √(x² - 1)(x^² + 4) In 1x + 11 + In |x-1| + tan-¹) + C Option 1 In x +11+ In |x-1|-tan ¹ () + C…

A:

Q: Calculate the area of the segment cut from the curve y = x(3-x) by the line y = x. 2 sq. units 1 and…

A:

Q: Calculate the gradient of f(x, y) = sin(x² - y) Vf=

A: Finding the partial derivative of the function.

Q: Use integration by parts to find the integral. (7x-3) e-2x dx -2x dx = (7x-3) e

A:

Q: 13. In |z|

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

Q: The following statements are true about "Integration" except: the method of adding or summing up the…

A:

Q: each of the following functions: (Use short (b) g(x) (a) f(x)=(5x³ + 2)(x²-3x+1)³

A:

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: -2 4.5×10 kg a. T= 2π 2.0×10³ kg/ s b. K = -(6.6×10² kg) (2.11×10¹ m/s)² = 2 -9.0×10 N·m²…

A:

Q: The integral of 2 raised to 4x dx with limits of 1 to 2 is equal to 85.6521 86.5617 86.1657 85.5621…

A:

Q: y = sinx, x = 0, y = 1; about y = 1.

A:

Q: Use a double integral to find the volume of the solid region under the paraboloid z = x² + y² and…

A: Use double integral concept