Direction: Compute the following limits: Given: 1 lim f(x) =5, lim g(x) = -9, lim h(x) = 6 1. lim(5 f(x)) f(x) 4. lim ( 5 g(x) · h(x)) g(x) 2. lim (f(x) • h(x)/ 5. lim(-3 h(x)²/)) 3. lim -4 g(x)

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A: Let's find. 

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Q: / 5x? tun(3x) dx. If u= 3x³, then the resulting integral is Jf(u) du. Find f Given: 5/2 A 18 B none ...

A: This question can be solved using the concept of substitution as used in integration.

Q: Question 9 5x2 tan( 3x) dr. ifu=3x*, then the resulting integral is SFlu) du. Find Given: A 18 none ...

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Q: 15. Scott Fallstrom once Epoke with his kids on the first day of the month of April about allowances...

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Q: 1. Consider the relation R1: R2 - R such that (r1, y1)R1 (x2, y2) if and only if both points are on ...

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Q: 3. a) Find the percentage error in computing u = Vx at x = 2.45, when x is 4 %3D b) | If Ax = 0.005,...

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Q: Question 5 5 Given: dx. Using u-substitution and transformation of integrand, what is u and du? 3/x ...

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Q: Use the following results, if needed, to determine whether each series converges or diverges. uk con...

A: (a) To test the convergence of the series ∑k=2∞1kln k5-1k5, we will analyze the convergence of the s...

Q: Use any method to determine whether the series converges or diverges. 00 (6k)! k=0 O The series conv...

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Q: Question 1 dx The integral can be re-written as A lim (-1+2 y 1-m m - 0 B none of the choices lim (2...

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Q: 1. What is (3x) ? 2. What is (x*+ x)? 3. What is (2-32)? 4. What is (6v - 3v + Sv)? 5. What is (x-1)...

A: As per the guidelines we can solve 3 parts only 

Q: Determine whether the series converges. k=1

A: We use limit test to find convergence or divergence of given series. Follow 2nd step.

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

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Q: d) If the coefficients are rounded off of 0.31x + 2.73 find the absolute and relative in y x + 0,35 ...

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Q: x²dx S: 1. 4 – 3 x' dy 2. V16 + y²

A: Let I=∫x24-x2dxI=∫x222-x2dxPut x=2sinudifferentiate dx=2cosu.duI=∫22sin2u22-22sin2u2cosu.duI=∫4sin2u...

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Q: (4x + 8x - 9x - 7)dx 2. 2x -1

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Q: 1. Consider the relation R1: R R2 such that (r1, y1)R1 (x2, y2) if and only if both points are on th...

A: We are given a relation  R1: R2  -> R2  such that any (r1, y1) , ( x2, y2) ∈ R2 are related to ea...

Q: 7. What is dx (x six(x)?

A: Since you have asked multiple questions in a single request we would be answering only the first (7t...

Q: II. Determine the derivative of the ff. logarithmic functions 4. y = 8 log , 7x² 5. y = - 5 log , (1...

A: As per our guideline we solve only first three parts

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Q: Calculate F . dS where F = (4x°z, 4y°z, 3z*) S is the surface of the solid bounded by the hemisphere...

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Q: 2. In each of the following, find fyzz, fæyx, fryz- 2. f(x, y, z) = ln(xyz) + z² tan-1(e"y)

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

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Q: Question 10 cot (2x) Evaluate the integral Vcot (2x)- 15 cse (2x) A) --Arcsec 4 4 cot (2x) B) Arcsec...

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Q: Express the surface area of the surface obtained by rotating the graph of y = 4 sin (x) for Sx as an...

A: To express: The surface area obtained by rotating the graph of y=4sinx for π6≤x≤π3. Concept used: Th...

Q: Use the formula for the binomial series: (1+x)" = 1+ mx + + ... 21 = 1+ Ein if al < I 1 to obtain th...

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Q: Solve the components of the given equation of conic sections and sketch the graph: a. x2 + y2 – 10x ...

A: Given

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Q: (x + 1)2 and the line (x+1)?, 1, where a is the same constant. 4. Let Si be the area of the region b...

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Q: Evaluate the following limits using L'Hôpital's rule   2. lim x→0+ tanh x/sechx − 1

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Q: Use the above theorem to find the sum of each series. NOTE: Write your answer in the form of a reduc...

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Q: Classify the series as absolutely convergent, conditionally convergent, or divergent. (-1)*+1k! (2k ...

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Q: Use the ratio test for absolute convergence to determine whether the series converges or diverges. I...

A: Ratio Test :  Suppose ∑ak be an series and            ρ = limk→∞ ak+1ak , then(i)  If ρ &lt;1 , then...