I. Evaluate the following limits. Using L'Hôpital's Rule is not allow 1+ 3/ 1. lim. 1 2x²+x-1

Q: . The voltage,V, in a circuit is slowly dropping at a rate of -0.01 volt/sec as the battery wears…

A: I have appended the formula used in the solution part.

Q: Using partial fraction in evaluating Ⓒ-1/2 (2x+1)+ 7/7/ A B 2x-6 © 1/2-(2x+1)= 1/7/2 D 6-2x…

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Q: 1 x√x²-2x =dx : √x²-2x x =+c C

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Q: 20 x³ dx (x²+4)5/2 (Use trigonometric substitution)

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Q: Describe the long run behavior of f(p) = (p+ 2)(p+ 4) (p + 5): As p →→ ∞, f(p) → ? ✓ As poo, f(p) →…

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Q: A b B d a The integral 15x²x³43x - 19 (x + 1)²(x² - 6x +13) can be rewritten as Ax + B D C + ax² +…

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Q: X A b B a C) C D d is solved by trigonometric substitution, which of the following (b) x = √5 sec8…

A: We can solve as follows

Q: Find all real solutions of the equation 8m² -18-374. Write your answers as a list, using a comma to…

A: A detailed solution is given below

Q: 14. Evaluate the following √x-²sec (+)tan ³ ( =) « dx 2tan (²) [7tan² ( ² ) +11] +C 77 2tan…

A: To evaluate: I=∫x-2sec41xtan521xdx Substitute 1x=t⇒-1x2dx=dt⇒x-2=-dt So, I=∫sec4t  tan52t…

Q: x² dx (x²+4)5/2 Sπ/4. (Use trigonometric substitution)

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Q: S Find sec42x -dx tanº2x cot²2x-cot82t+C 12 16 1 1 1 1 12 tan 62x 16 tan 82x --(cot$2x) (² 1+3csc²2x…

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Q: Find the exact arc length of the curvex = 1 3(1² Enter the exact answer. L = + 2)² from y = 1 to y =…

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Q: Find the radius of convergence, R, of the series. 8 n Σ (x-a)", b>0 bn n = 1 R= Find the interval,…

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Q: ♫/² sin ( cos() sin (²) dx (Consider initially the first 2 terms)

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Q: Consider the integral f sin-¹x dx. If we let u = sin ¹x and dv = dx, the integral can be written as…

A: The given integral,  ∫sin-1x dx

Q: (3x-x²) dx x² Reciprocal Substitution

A: Let's find.

Q: Question 4 Solve the equation: 1²+t+19-0. Fully simplify all answers, including non-real solutions

A: The given equation is: t2+t+19=0

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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Q: dx Arcsin (²) + c

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Q: b) Determine whether the series n=1 find its sum. Show All Your Work! n-1 (-3)* 4" is convergent or…

A: We need to determine convergence.

Q: ... : S (1 + 2x) e-x dx. Using integration by parts and letting u = -1- 2x, dv = 2 f(x)dx, then the…

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Q: (D² – D − 2)y = cos x

A: Here is the solution:

Q: Given f(x)=√x-5;x#5 and g(x)=x+3. Find the domain of (gof)(x)?

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Q: Given The boundary of C: 0 ≤ x ≤ π,0 ≤ y ≤ sinx With Green's Theorem, Evaluate this line integral. $…

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Q: Write an equation for the quadratic graphed below: x-intercepts: (-1,0) and (4,0); y-intercept:…

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Q: x²+x+1 Sa 2x²+2+3+x A B cb dx g(x) - dx = [Aƒ (x) − B ln(g(x)] + D fb da, and if A = ‚B <0, then dx…

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Q: Find F'(x). SOLUTION IN HANDWRITTEN x 1. F(x) = sin √t dt 2. F(x) = sin t² dt

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Q: dp p(-75+25p²) 2 S. Trigonometric Substitution

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Q: II. Find 2. y = Do not simplify your answers. dx tan ¹(cosha) (sin² x)(secha)secz [use logarithmic…

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Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not allowed. 3. lim x-3 (x-3) tan(9-x²)…

A: As L'Hospital's rule is not to use so I have used the expansion of sin and tan function and easily…

Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not allowed. 2. lim (√²-x-√√x² + x)

A: The given limit,     limx→-∞x2-x-x2+x

Q: dx3 d²y_dy+y=0 dx² dx

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Q: If f cos*2t dt = At-B sin 2t cos 2t + D sin 4t cos 4t + C where A, B, C and D are constants 24-38…

A: This is a problem related to integration of the trigonometric function. Based on the general formula…

Q: Find Do not simplify your answers. dy da 1. log;(√2x² + y) + tan(x² − 7") = sin¯'¹(x² − 1) + ½

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Q: log(x+3) z-1-1-cosh(cos-12) 4. lim

A: Given,            limx→1-log12x+31-coshcos-1x

Q: x²√√2x-x² dx

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Q: f/²sin (co COS () sin (²) dx (Consider initially the first 2 terms) ATT/A a dr

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

Q: S sin (Inx) dx? How many times will you perform integration by parts to evaluate

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Q: IV. Do as indicated. 1 1. Let f(x) Find the equation of the tangent line to the graph of f'(r) at…

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Q: Given: (1+2x) ex dx. Using integration by parts and letting u = -1-2x, dv = f(x)dx, then the value…

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Q: Explain why you think the sequence -2, 25 125 " ... 8 2 32' . converges to a finite number or…

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Q: The IBP formula fudv=uv-fvdu Which of the following statements fits and satisfies the equations? can…

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Q: Solve 4t² +8t+4= 0 by using the square root method. Hint: complete the square first! Enter each…

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Q: Check if proper fraction. 2. Check if the denominator is reducible or not. 3. Perform cancellation…

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Q: quotient (Express numbers in exact form. Use symbolic notation and fractions where needed.)…

A: Given query is to find the derivative of the expression.

Q: 18) fin

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Q: 7. f(x) = 3√x; [1,4] 8. f(x) = x-2/3; [1,27]

A: We can solve this as follows:

Q: The equation 2k² - 3k 10 = 0 has solutions of the form k N± √D M (A) Solve this equation and find…

A: The given equation,    2k2-3k-10=0

Q: 20. To solve S for this integral? A(2x) + B x² A. B. C. 22-12x dx, partial fraction is to be…

A: The given integral,      ∫22-12xx23x2-10x-8dx

Q: The height y (in feet) of a ball thrown by a child is 1 y 162² +42 +5 where a is the horizontal…

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