5. fe²x sin x dx 2x

Q: Determine the values of m and b such that function g is continuous at every real number: if r 1.

A: Since the function g is continuous.So, limx→1-g(x)=g(1)limx→1-x2-mx=-212-m(1)=-2m=1+2m=3

Q: (b) Find the points on the given curve where the tangent line is horizontal or vertical. r = 1 + cos…

A: We are given a curve in its polar form  r= 1+cosθ We have to find points on the curve at which…

Q: y² = x and y² = 2 − x

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Q: A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.4 cm/min.…

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Q: Suppose that fn ⇒ f on R and that each fn is a bounded function. Prove that f is bounded.

A: Solution

Q: 3.§ sin* 2 x sin 4 xdx

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Q: Find the absolute extrema of f(x) = x³ - 6x - 1 on the interval [-2,3].

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Q: Problem 7 Ső S xvx² + 1 dx

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Q: What integration technique can be used to integrate: 5√3+x² dx X

A: Follow the procedure given below.

Q: (c) Show that the function is a solution of the differential equation (−1)" x2n f(x) = Σ (2n)! n=0…

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Q: (x²-1) + 2y = (x + 1)² dy dx

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Q: Use the trapezoidal rule with n = 20 subintervals to evaluate I = -5 sin² (√0× t) dt

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Q: Show that for all n € N, one has 1 2√n+1 <√n+1-√n<; 2√ñ

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Q: Q1: A. Find the general solution of the following Initial Value Problem (IVP): y+9y-10y = -40t²-72t…

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Q: (b) In +8 x² 2 - 36

A: We have doing solution useing logarithm laws

Q: The partial fraction decomposition of f(x) g(x) + where 3 (x + 3) (x² - 4x + 4) f(x) = g(x) = -3x² -…

A:

Q: Find the volume of the solid generated by revolving the area bounded by the given curves about the…

A: Given problem:- Find the volume of the solid generated by revolving the area bounded by the given…

Q: Q4: If f(x,y) = x²y + exy Siny Find 1) 2) (D = f), at po(1,0) in the direction of 0 = Po

A: Given problem:-

Q: A company's revenue from selling x units of an item is given as R = 1800x – 2x². If sales are…

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Q: a problem of physical  phenomena that can be solved as differential equation using Euler method.

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Q: 90 y 2 1980

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Q: e dy dx У-х+1 У-х +5

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Q: In pair, study and find the integral of the following functions. You will be awarded marks for each…

A: We have to solve integration  As per Bartleby guidelines we have to solve 1 question if you need…

Q: Use the elimination method to find all solutions of the system: [x² + y² = 7 x² - y² = 4 The four…

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Q: s={ 3112 4'2'3'9' =(5, 5.5, 6, 6.5, 7, 7.5,...} = {√2,2√2,3√2, 4√2,...} ={√2,2,2√2,4,...}

A: Topic:- sequence and series

Q: The current population of a small town is 3947 people. It is believed that town's population is…

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Q: g(x) = 3 ln(x - 2)

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Q: dx 15. S (x²+36) ³/2

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Q: For the given function f(x,y)=x²y³+3x³y, find a flay

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Q: A fifth degree polynomial with constant coefficients may have (1) 5 distinct real roots. (II) 3…

A: This question can be solved by using the concept of nature of roots of n degree polynomial.

Q: An airplane is heading north at an airspeed of 500 km/hr, but there is a wind blowing from the…

A: We have to find the angle and speed of the plane.

Q: (D² + 3D + 2)y= sin ex

A: The given differential equation is  (D2+3D+2)y=sinex

Q: (c) Express the number 1.234567 as a fraction (in its simplest form) using the sum of a geometric…

A: Ans=45679/37000 For detail...go through the solution.....I have solved step by step in detail

Q: 6. Use the definition, determine whether the function g(x) = x = 2. Justify the conclusion. x² -…

A: The solution is given in the next step.

Q: (D6 + 8D4 + 16D²)y = 0

A: We have to solve the given D. E.

Q: 7. f sec5 2 t dt

A: We can solve the integration as below

Q: Q2: Evaluate the following integrate: 2- S(2 + 5x) es dx

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Q: 4. 2x3ý = y (y² + 3x²)

A: The given differential equation is  2x3y'=y(y2+3x2).

Q: Find the altitude of a rectangular closed box with volume 100 cubic inches with length twice the…

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Q: (e) Find the exact length of the curve. x = e cost, y = et sint, 0 ≤ t ≤n.

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Q: Given f(x,y)=x²exy, evaluate f,(3,0). (A) 27 B) 13 C) 9 D) 6

A: The function is given as , fx,y=x2exy evaluate fy3,0=?

Q: Solve what is asked in the following problems. Write your solutions and box your final answers 1.…

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Q: Arrange the choices in order 1.2.3.. to prove: For any sets A, B and C A x (BUC) = (A x B) U (A x…

A: Here we have to arrange the option.

Q: Used Cramer's Rule to find the value of the variables (X,Y,Z) in the following equations x + 2y + 3z…

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Q: A man that is 5 feet tall is walking in a straight line at a rate of 3 ft / s towards a lamp post…

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Q: (d) Find a vector function that represents the curve of intersection of the two surfaces: the xy…

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Q: 3: Fill in the blanks in the following: 1 3. 4. If = (-12, 4, 8) the position vector of u…

A: Topic:-  vector algebra

Q: 11.J sin 3 x sin 6 xdx 3

A: To evaluate the given integral.∫sin 3x sin 6x dx

Q: d²y dy 4. (a) Compute the general solution for: +4 dt +3y=e-t/2. dt² (b) Compute the solution with…

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

A: To find the absolute maximum and minimum values of the given function: fθ=sin θ; -11π6≤θ≤-π2 Here,…