Using the definition of derivative, find functions: a) y = xVx -2 .2 (b) y =- (x-1)

Q: (a.) the critical

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Q: Consider (x8+ 8x5+ 16x2) ² -dx. Using u-sub

A: Given: - The integral is, ∫x2+1xxx8+8x5+16x22dx To find: - The values of k and n. By using u-substit...

Q: b. Recall that f(x) = 2*-1 - 1. Graph of f,(x) = f(-x) + 2, f2(x) = f(-x+ 1) +1, and fs(x) = fi(x) +...

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Q: Complete the table by stating whether the equation is ordinary, partial and linear and non-linear. A...

A: The given differential equation is;. t2s"+ts'=4-3sint.

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Q: Question 7 dx 7-9e-2x Using u-substitution and transforming the integrand, find du. Given: A 14e2xdx...

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Q: Use the Squeeze Theorem to evaluate lim sin(tan r) sech(secr). ес

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Q: Determine whether the series converges, and if so find exactly its sum. Otherwise type none in the b...

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Q: One model for the spread of a rumor is that the rate of spread is proportional to the product of the...

A: Let's find. 

Q: dx The integral can be re-written as. VI- A lim (-2+ V1- m) m-- 00 B none of the choices lim (2-2 V1...

A: ∫-∞0 dx1-x  

Q: A 14 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 4 ft/s, how ...

A: A 14 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 4 ft/s, how ...

Q: show that for positive epsilon, |x-4| |3x-12|<e

A: a⇔b implies if a holds then also b holds and vice versa.

Q: 8. What is de x2+1

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Q: Find the nth Taylor polynomial for the function, centered at c. f(x) = In(x), n = 4, c = 6 Pa(x) =

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Q: For each problem below: a) Determine the indefinite integral (do not include the "+c" and do not inc...

A: a. ∫4sinx+7cosxdx=4-cosx+7sinx=-4cosx+7sinx

Q: Consider the integral dx . Using u-substitution, what is the appropriate u and du? -2x 3e 2t 2e

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Q: Use sigma notation to write the Taylor series about z = 1, for the function. 3 In z; z0 = 1 k =

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Q: A vertical wall makes an angle of radian measure ?n with the ground. A ladder of length 20 ft is lea...

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Q: Solve the following, glving the solutlons In the form ptqvr 6x +15 Rationalise the demoninator of th...

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Q: a. Show by means of slope that the four points (0,0), (-2,1), (3,4), and (5,3) are vertices of a par...

A: This is a problem related to geometry. For parallelogram opposite sides are parallel to each other. ...

Q: Use the definition of Taylor series to find the Taylor series (centered at c) for the function. f(x)...

A: We find out the Taylor series of e5x at c=0. Follow 2nd step.

Q: Topic: Integration by parts. Evaluate the integral.  Given:  ∫ x tan−1 x dx

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Q: dx du Sk , where u= f(x), and for some constant, k. Compute. f(2). The integral reduces to ex +1 e +...

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Q: Prove that the following statement is true for all positive integers. 1 1 1 + + 4 8 1 2" – 1 + 2n Pn...

A: Given; Pn : 1/2 + 1/4 +1/8 +...+1/2n =(2n -1)/2n

Q: evaluate the definite integral by interpreting the graph of the function over the indicated interval...

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Q: ergence and the interval of convergence. Test for Absolute Convergence to the given series. The

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Q: Name: Section: Find the derivative of the following. Show your solutions. 1. What is (3x) ? 2. What ...

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Q: Estimate the maximum volume of a conical pile of road salt that can be stored on an area in the shap...

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Q: dx The integral k, where u= f(x) and for some constant, k. Compute 2). reduces to ex + 1 A е - 1 B n...

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Q: sin(2a)dx + cos (3y)dy 3 0, у(т/2) — п/3 ||

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Q: (-1)+16· 13 . 20.(7k – 8) * Use the formula for the binomial series: (1 + x)" = 1+ mx + m(m-1) m(m-1...

A: solution:-1+xm=1+mx+mm-12!x2+ ... mm-1...m-k+1k!xk              1+∑k=1∞ mm-1...m-k+1k!xk         if ...

Q: Given the function f(x) = 3 x3 + 7 x2 + 3, 8 4 -2.5 -2 -1.5 -1 -0.5 0.5 1 calculate the critical val...

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Q: 2. Find the equation of the tangent line to the curve at the given point by eliminating the paramete...

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Q: (d) The function k(x)is defined as follow: 3 x+ 17 -- 4 k(x) = { 2, x =1 5|x-1| x² -1 x>1 Discuss th...

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Q: Evaluate the following limits using L'Hôpital's rule 1. lim x→0 e^x(cschx)

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question fo...

Q: Water is running out of a conical tank 3m across the top and 4 m deep at the rate of 2m3/min. Find t...

A: Here, the volume of the conical tank is: V=13πr2h   ...(1) Here, here triangles ABC &amp; DEC are s...

Q: ne sketch. base 120 130 140 QUESTION 6 Water is scarce in South Africa. The annual average rain fall...

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Q: 04) Prove that 1- Cos + x) = sin x, 2- (sin x +cos x) sec x = sec2 x %3D

A: We have to prove that following trigonometric identity.

Q: Complete the table by stating whether the equation is ordinary, partial and linear and non-linear. A...

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Q: 1. Let (r + 2)², if I 0. (a) Give the r coordinate(s) of the possible point(s) of discontinuity of ...

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Q: Find the nth Maclaurin polynomial for the function. f(x) = e-X, n = 5 2 3 4 5 P5(x) = 1-x+ 6 24 120 ...

A: Note that, the function ex is: ex=1+x+x22!+x33!+x44!+x55!+...⇒e-x=1+(-x)+(-x)22!+(-x)33!+(-x)44!+(-x...

Q: Find the nth Taylor polynomial for the function, centered at c. f(x) = In(x), n = 4, c = 4 Pa(x) =

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Q: Find the interval of convergence of the power series. (Be sure to include a check for convergence at...

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Q: If the solution to e2x sec2(e2x+1)dx is equal to ktan (e2x+1) + C, find the exact value of k. 1 (A) ...

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Q: Question 12 For the following function , find the equation of f-(x) and hence show that f({=}) = f (...

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Q: n2 - 6 with n5 + 6 Write an inequlity comparing for n > 1. n3 (Express numbers in exact form. Use sy...

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Q: When is an equation considered as a solution of  differential equation?

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Q: Consider -dx. Using u-substitution and transformation of integrand, then the power formula applies; ...

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Q: State whether the following series is Convergent or Divergent. (-1)" Vn +1 n=1

A: Absolutely convergent :If the the mod of the alternating series ∑n=1∞(-1)nan i.e., ∑n=1∞|(-1)nan | =...

Q: A cylinder is inscribed in a cone as shown in the figure. The radius of the cone is 3 inches and the...

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