Show that the curve  x = 3 cos t, y = 4 sin t cos t  has two tangents at (0, 0) and find their equations. y =  −43​x       (smaller slope) y =  43​x       (larger slope) Sketch the curve

Q: 1. The figure below shows the graph of f', the derivative of the function f, on the closed interval…

A: Given

Q: Consider the function f(x) = 4x + 2. (a) Estimate the area between the graph of f and the x-axis…

A: given f(x)=4x+2a=0 to b=3n=6 (no. of rectangles)Δx=b-anΔx=3-06=12

Q: 0.602x(3×3!/4)=? (Gamma function)

A: This question can be solved using the formulas related to gamma function

Q: 3. Find all values of m so that the function y = tm is a solution of the equation 3t²y" +11ty' − 3y…

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Q: The graph is a transformation of one of the basic functions. Find the equation that defines the…

A: We need to find equation.

Q: A metal rod is placed in an oven and the temperature, T (measured in degrees celsius), of the metal…

A: Given ,  A metal rod is placed in an oven and the temperature, T (measured in degrees celsius), of…

Q: A light year is the distance light travels in a year. What is a light year in km? The speed of light…

A:

Q: need

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Q: Identify the special angles above. Give your answers in degrees in the range [0,360). A: B: C: D: E:…

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Q: Needed to be solved correctly in 10 minutes and get the thumbs up please show neat

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Q: Sketched below are the graphs of f(x)=x²-1 and g(x)=x+1., The graph of fintersects the x- axis at A…

A: Given data:- The given equation, f(x)=x2-1g(x)=x+1

Q: Q5/: Find the general solution of non-homogenous differential equation using Variation of Parameters…

A: Solution is given below:

Q: The graph of f is shown on the coordinate plane. Selected values for g are shown in the table. Graph…

A: Given graph:-

Q: Wrong answer

A:

Q: The line whose slope is 3 is tangent to the curve y=x² + 3x + 2 at the point, O (3,-2) O (-3,2) O…

A: The line whose slope is -3 is tangent to the curve y=x2 +3x+2 at the point. Here slope and line…

Q: 1. yp1: = 1 (+ dx (x+1)³(2x-1)³ find the derivative and save as yp1

A: Given yp1=ddx1(x+1)3(2x-1)3

Q: Using distance formula, prove the Apollonius' theorem that is in AABC, AB2+ AC² = 2 (AD² + BD2),…

A:

Q: Find an equation of the plane. The plane that passes through the point  (−2, 1, 3)  and contains…

A: Question : Find an equation of the plane.   The plane that passes through the point  (−2, 1, 3)  and…

Q: X Given zx 2cos u; y = 3sin v, find y O-2cos u cos v 3 sin ² v O 2sin v 3 sin u O-2sin u 3 sin v…

A:

Q: Refer to the figure and find the volume generated by rotating the given region about the specified…

A: We have to find volume generated by revolving R1 about line AB.

Q: Evaluate the following relations for given values f(x) = 3x² - 2x (a) Find (b) Find f(x + 2) f(1 -…

A:

Q: V₁= 2³²-37²³² +27= 0 + 1 (1-1)(1-2) = 0. 1₁=0, A2=1, d3 = 2 X 2X X Y₁(x) = C₁ + c₂e² +₂²² +₁=1, 4₂-e…

A: The objective of the question is simplying the given integral.

Q: Suppose y sec-¹x. Then a arcsec O sec y Y sec Y

A:

Q: Let g(s, t) = (sin(s)-t, e, s) and f(x, y, 2) = e²+²y+z Compute(fog) at (0,0).

A: See the details solution in belo

Q: 7. f is a differentiable function on the interval [0, 1] and g(x) = f(4x). The table below gives…

A:

Q: An integrand involving a radical form √√49-16x² suggests the substitution ○ 4x = 7 sec Ⓒ O x = 4 sin…

A:

Q: Let lim f(x) = 19 and lim g(x)= 16. Use the limit rules to find the following limit. X-9 X-9 lim…

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Q: 27. A large tank is partially filled with 100 gallons of fluid in which 10 pounds of salt is…

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Q: Question Find the area of the region that is bounded above by the curve f(x) = (x+3)² and the line…

A:

Q: Question Find the area of the region pictured below that is bounded by the functions f(x) = x² - 6x…

A: Topic - Area Bounded by curves

Q: 3. Consider the initial value problem (IVP): ty' — y = t²e-t, y(1) = −1. (a) Use integrating factor…

A: We will use integrating factor method to solve this.

Q: +1 √2 1337 =?

A: Given i+121337

Q: 22 e 1-§ 2(2-21) ² c: |z_11 = 1/2, 17-11-2

A: The given integral I=∮Ce2zzz-2i2   ;  C=z-i=12, z-i=2 Cauchy integral formula:   suppose that C is…

Q: Solve the differential equation. y' + y tan x = cos X, -π/2<x<π/2 A y = x cos x + c cos X, - B) y=x…

A:

Q: Express the following functions in the form U+iv f(Z) = ln (1+z) ●

A: The given function is fz=ln1+z.We need to write it in the form u+iv.

Q: Find median and mode of the messages received on 9 consecutive days 15, 11, 9, 5, 18, 4, 15, 13, 17.…

A: Please check the given options because the answer to the given question is not among the given…

Q: Calculate the angle between the normals to the surfaces x²y + z = 3_ and x log z − y² = −4 at the…

A: Angle between two normal vectors a and b is  θ=cos-1±a·b

Q: 1. Find the limit if exists or show that the limit does not exist 1-cos(x+2y²) (x+2y2)2 (a) (b) lim…

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Q: H

A:

Q: Find all values x = a where the function is discontinuous. For each value of x, give the limit of…

A: We have to find all values x = a where the function is discontinuous f(x) = 3x2 + 8x + 4

Q: If  g(x) = x2 + 10x  with  x ≥ −5,  find  g−1(56).

A:

Q: Prove that sinh−1(x) = In( x+Vx2 +1)

A:

Q: Evaluate the following integrals. b. "f2 sec² xdx (2x+5)dx

A: Topic:- application of integration

Q: 4. Find all functions that solve the differential equations. (a) x' = te-2t (b) x' = 1/(tlnt). (c)…

A: To find the functions that solve all the differential equations

Q: Find the value of c such that enc=14 n=0 Enter an exact value BD

A: Given :∑n=0∞enc=14

Q: Convert 1.2 in radians to degrees:

A:

Q: = Find the area of the region pictured below that is bounded by the functions f(x) = x² - 9x + 20…

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Q: Find the center and radius of the circle. (x - 3)² + y² = 36 center (x, y) = radius Sketch the graph…

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Q: Question Write the integral required to find the area of the region pictured below that is bounded…

A:

Q: Consider the function defined as follows: f(x) = 7x² - 9. f(x+h)-f(x) h Find the limit of O 14x 2x+h…

A: