1. Consider the function f(x) whose graph is given below. If a discontiuity is Emumerate all discontinuities of f(x) and identify their types. removable, state the redefiniton that will remove it. Hint: There are 6 discontinuities.

Q: Consider the following function. f(x) = −x2 − 14x − 9 Find its average rate of change over the inter...

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Q: Given the ordered pair P, determine the requested sin, cos, or tan of angle . P(6,-5) cos = (5√61...

A: We have to calculate r then we can find trigonometric value. 

Q: Use Green's Theorem to calculate (4z? - 3yz)dr + (3zy + Vy? + 6)dy, where Cis the circle (r – 1)2 + ...

A: Greens theorem

Q: Solve the components of the given equation of conic sections and sketch the graph а. х — -y2 +1 b. x...

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Q: Pinocchio’s nose length y (in inches) is dependent on his lie count (s). Geppetto has modeled this ...

A: Given equation, yy=as where, y is Pinocchio’s nose length (in inches) s is his lie count a is a magi...

Q: dx Given: - 06-2x. Using u-substitution and transforming the integrand, find du. A 14e2xdx B 18e-2xd...

A: Given:  ∫dx7-9e-2x To Find: By using u‐substitution and transforming the integrand, to find du.  

Q: Factor the difference an+1 - an to show that the given sequence {an} is strictly increasing or stric...

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Q: Show that for all positive integers n, 13 + 2° + ...+ n³ = (1+2+3+ ...+ n)?

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Q: EC an

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Q: 2. Find the indicated limits of the following algebraic and trigonometric functions: x' -1 а. lim. -...

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

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Q: Question 2: Differentiate the functions by using product or quotient rule. a) f(x) = (1 – 3x²) · e* ...

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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: a2/2 if l띠 3. Find vertical asymptotes, if any, for y = f(x). Find oblique asymptotes, if any, for ...

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Q: ry' – y = x²e=z

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Q: y' + y = 5 sin(2x)

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Q: Suppose f(x) - 6'Vi+ť' dt. 1) Evaluate / (2).

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Q: The diagram below shows points P, Q and R. The coordinates of the points are given by P ,Q(5, 6) and...

A: The solution is given in the next step.

Q: sin 3x Given: -dx What is the appropriate formula to find the integral? cos? (3x) (4-3 sec 3x) du (A...

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Q: I. Determine the derivative of the ff. exponential functions 1. y = 8 e -4x 2. y = 15 e 7x + 3 3. y ...

A: As per our company guidelines we can answer only three subparts question at a time, but if you need ...

Q: Using u-substitution, the integral Jf(x)dx reduces to a new integral J glu) - , evaluate the new int...

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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: Use Gauss' Divergent Theorem to calculate F. dS, where F = (2x + sen (e+1)) i+ 3yj+ cos(z?)k and S i...

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Q: Find the distance between the points (distance formula) 5.(2a+c, 2d), (2b-c, 2c) 1.(3, 2), (4, -3)

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Q: Calculate y°dz – yz²dy – sen(2)dz, where C'is the path connecting the point A(-2, 2, 4) to the point...

A: We will calculate the integral ∫Cy2dx-yz2dy-sinzdzwhere path starts from point A-2,2,4 to the point ...

Q: 1 Use the Cauchy's integral test to show that Σ diverges n. In n. In In n n=2

A: Cauchy -Integral  Test series ∑n=1∞ an      converges if integral ∫1∞ f(x) dx finite and  diverge if...

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: Express the repeating decimal as a fraction. 0.4713 43 43 43...

A: In this question we have to express the repeating decimal as a fraction.

Q: Question 2 12x +1 dxp. (2x- 1)2 (3x + 2)² Evaluate:

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Q: following: (a) y = \f(x)| (b) y = f (x) (c) y = JF(x). f(x) y = 2 3

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Q: tan (In 4x) cos (In |(2x)"|)|+C. what is b? The integral of dx is b In A B 2 4 4

A: Given :  ∫tan(ln|4x2|)xdx=bln(|cos(ln|(2x)a|)| +C   To find : Value of b  

Q: 3/2 X2 dx

A: 1.∫x32tan-1(x) dxlet x=tdiff o.b.s12xdx=dt dx=2t dt∫t3tan-1(t) 2t dt=2∫tan-1(t) t4 dtwe know that ∫u...

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: A. Find the value of a to make the lim f(x) and f(c) equal at all possible value of c within the giv...

A: Note : As per our guidelines we are supposed to answer only one question if there are multiple quest...

Q: x4 + 2y = x2 – x +1 y(1) = 1/2 dr

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Q: Find the equation of the tangent to the following curve at the point where x = 1 y=Vx

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Q: 8. What is de x2+1

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Q: Direction: Compute the following limits: Given: 1 lim f(x) =5, lim g(x) = -9, lim h(x) = 6 1. lim(5 ...

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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: Use the binomial series to find the Maclaurin series for the functi 1 f(x) (1 + x)3 |(2-3) f(x) = Yo...

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Q: Determine whether the series converges, and if so find its sum. If the series diverges, indicate tha...

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Q: Given: 5x2 tan ( 3x) dx. If u=3x³, then the resulting integral is Jf(u) du. Find. 4

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Q: dx Given: 7-ge-2x. Using u-substitution and transforming the integrand, find du. A 18e-2xdx B - 18e-...

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Q: 10) Construct a Pictograph illustrating the information provided in the chart. Label the pictograph ...

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Q: Directions: Determine whether the given function is a. continuous or not b. differentiable or not. A...

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Q: Question Define Q as the region that is bounded by the graph of the function g(y) = - Vy – 1, the y-...

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Q: Answer this question by showing all work and formulas used to solve both derivative functions and si...

A: Given,           f'x=32x3+126x23-4x2+2x3+1323-4x-4           g'x=4x-1-12+4x+1-12x-1-32To find : Simp...

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: Consider the linear programming problem: Мaximize P-х +1.2y Subject to 2x + y < 180 (constraint 1) x...

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Q: x³dx (v²– 1)7 3.

A: In this question we have to find the value of Integration.