Consider the function f(x) = x - x³. a. Determine the absolute extremum using the First Derivative Test, if there are any. b. Sketch the graph of f.

Q: 7. Find the limit, if it exists. If the limit does not exist, explain why. (a) lim sin (2x6) sin(4x…

A: Explanation of the answer is as follows

Q: 2. f(x) = 3x4 +√4x; f" (1.2) 6

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Q: A projectile is fired vertically upward with an initial velocity of 210 m/sec from a point 2 m above…

A: topic- algebra

Q: 1. Determine the infinite (oo or -o) limit as follows: x² - 2 (a) lim x2-x² - 3x + 2 sin x 1 x+ cos…

A: Topic = Limits

Q: 5.12 7 ln 3x dx X

A: Is multiple questions are posted we are allowed to solve only 1st question...so please upload again…

Q: 2 -dx for n=4 is equal to Blank 1 (use 2 decimal places with (x+2)² Using Trapezoidal method S…

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Q: 11 lim 348 n=0 tan ²¹ (-1) + tan²¹²¹ (1) - tan¹ (2n+1) - tan²¹ (2n + 3)] ??

A: To explain the circled part.

Q: * 5.8x √4x²+5 dx 2(4x²+5)³/2 A. +C 3 O A. OB. O C. * 6. f 35x-1 A. 35x-1 In 3 O A B 5x-1 dx C + C…

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Q: Question 1 Iff and g are continuous on [a,b] and f(x) ≥ g(x) for all x € [a,b], then [f(x)dxz g(x)dx…

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Q: The curve y = √x + 2 is revolved about the y-axis from x = 1 to x = 8, find the surfac area.

A: Here we have to find the surface area.

Q: ←…

A: Given

Q: A) Link between plane and line in the differentiation. 7) Find the aquations of alono pocinh the…

A: Link between line and plane.

Q: Problem 3. A boat on the ocean is 4 mi from the nearest point on a straight shoreline; that point is…

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Q: Which of the following is not true? 5 dx dx (A) lim S o 25-x² c+5-0 25-x² 3 dx dx So in (x²) B √₁…

A: We have to determine integration

Q: pair of parametr quations is given. x = e4t y = et (a) Sketch the curve represented by the…

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Q: Prove that the equation 3x² – 3x + 2 = 0 has a solution on interval [0; 1].

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Q: State the domain, vertical asymptote, and end behavior of the function. g(x) = ln (6x + 12) + 1.3…

A: Domain of a function:-  Set of all values of independent variable such that function at that point…

Q: If you evaluate the integral expression S 4x +3|dx the result is Blank 1 (use fraction or decimal in…

A: The integration of the integral is |4x+3| limit from -1 to 1.

Q: problem. Check that the following Function is harmonic and determine it it is a harmonic Conjugate.…

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Q: Find the intercepts and the vertical asymptote of x²-2x-3 4 Enter the intercepts as points. (a, b),…

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Q: Find the transition points. y = 4x7 - 56x6 (Use symbolic notation and fractions where needed. Give…

A: Given that y=4x7-56x6Solution :if we find critical point then f'=0 and f' does not…

Q: Solve for x. O-1,-4 O -1,4 O 1,4 O 1,-4 x-1 3 2 x-2 =0

A: Given,      x-132x-2=0

Q: If you evaluate the integral expression 12x+1|dx the result is Blank 1 (use fraction or decimal in 2…

A: We have to integration

Q: Find the area bounded by y=√x and y=- ·x 2 (A) 4/3 B 2/3 C) 10/3 D) 5/3 E None of these

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Q: State the domain, vertical asymptote, and end behavior of the function.   g(x)=ln(2x+12)+1.8…

A: This question is related to Functions, we will solve it using given information.

Q: Use Figure 1 to evaluate each trigonometric function of angle A. The side adjacent to angle A has…

A: As we know that; The trigonometric ratios;…

Q: 4. fx√x - 3 dx

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Q: A bucket is filled with sand so that the total mass (sand and bucket) is 15 kgs. The bucket is to be…

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Q: Find the complete solution of ds dt = 5t* √s.

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Q: the following function problem: check that the is harmonic and determine it it is a harmonic…

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Q: Use Figure 1 to evaluate each trigonometric function of angle A. The side adjacent to angle A has…

A: We will use simple trigonometric formulae to solve this question.

Q: c) The equation of a straight line, of gradient m and intercept on the y-axis cis y = mx + c If a…

A: Let's solve.

Q: What integration technique can be used to integrate: O Integration Formulas O Trigonometric…

A: Ans=Trigonometric substitution  For detail...go through the solution....

Q: This answer is incorrect do you know why?

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Q: Find a particular solution of ds 1 dt =cos-t determined by s=3 when t == 2 3 wha

A: Given ,    dsdt=cos(t/2)

Q: y = √√2x + 7

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Q: In|x| 10. x A. In |x| + C dx B. In² x + C C. In² |x| 2 + C

A: We need to find integral.

Q: Solve the differential equation: (2x - 4y - 3)dy=(x-2y)dy

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Q: To integrate x3x² dx' Ox хех2 242 x² OX we apply integration by parts and in the form u dv, dv is…

A: We have to determine the integral

Q: Find the complete solution of ds dt = 5t* √√s.

A: Given problem:- Find the complete solution of dsdt = 5t4√s

Q: Find the derivative of Ox²2cosx + 2xsin x O 2xcos x O x² sin x + 2xcos x O x2cosx y=x²sinx

A: We know that if f(x)=g(x)h(x) then  f'(x)=g'(x)h(x)+g(x)h'(x)

Q: solve this. Find the absolute extrema of f on the given interval. (find the absolute maximum value…

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Q: Using Trapezoidal method √x dx for n=4 is equal to Blank 1 (use 2 decimal places with proper…

A: We have to find the value of the integration ∫01x dx  with n=4  using trapezoidal method. From…

Q: 4 3. 2 1 -4 -3 -2 -1 2 -1- -2- -3+ 3. From the above graph of y = f(x), find the following limits:…

A: a)2  b) -2  c) -4

Q: Write the complex number in polar form with argument between 0 and 2. 5/(1 + i)

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Q: If f is continuous on [a,b], and f(x) > 0 then b [²√f(x) dx = a √5°₁ S f(x) dx

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Q: Which of the following is not true? (A) None of the given choices 3 dx dx Ⓒ = S B S³ = In(x²) lim c→…

A: All Option are  correct So we have to choose Option 'A'

Q: Consider the power series. $Σ (-3)^(x-2)^. √n+2 n=o 1. Use Limit Comparison Test to show that the…

A: Note: In the second circled part the student has made an typing error by writing 'x' in the…

Q: 7. ydx-xdy + xydy = 0 Ans: In²+ y = c

A: We have to solve differential equations

Q: Given the function y=f(x), y" is found to be negative over the interval (4,8), then over this…

A: Answer is given in next step.