Consider lim e-. a) lim 4x - x² = 0 b) If we let t = 4x - , then we can rewrite the limit as lim of

Q: 4. Find the limit: lim (b) lim -5x+4 x-4 X-4

A: We can find the limit using the L'Hospital rule.

Q: The cost of certain piece of machinery is S 700 and its value is depreciating with time according to...

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Q: find the constant term of (2x² + 1/x)⁹

A: find the constant term of (2x² + 1/x)⁹   

Q: The graphs of the first and second derivatives of a function y = f(x) are shown to the right. Sketch...

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Q: 2 91 If A = 1+y 4 0 and B = 5 3 31 [0 2 91 40 find the values of x, y. l2 3 3] x2 2

A: We have to find X , Y values  

Q: The function below is continuous at every real.number. Find the value of (m + 3/2). 1– 2x if x >4 mx...

A: We have to find 

Q: Given the differential equation d?y 12. + 4y = 0 di? Determine the Characteristic Equation for the g...

A: We have to find characteristics equation

Q: If [ s( ) d0 = –sin20 + C , then f (0) =-cos20. 2

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Q: What is the volume of the solid generated when the region in the first quadrant bounded by the graph...

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Q: If convergent evaluate

A: Given, ∫-232x4dx

Q: A. Write T if the statement is true; otherwise, write F. 1. f(x) =, lim f(x) = f(2) 6+4t 2. lim t-3 ...

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Q: Solve the homogeneous system of equation а — 3Ь + 7е%3D 0 - с — 2е — 0 d — 10е — 0

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Q: Evaluate the given function ſ sec5xtanxdx a. sec*x + C b. sin*x + C c. cosx + C d. 금esc5x + C

A: topic - indefinite integral

Q: driver driving along a highway at a steady 41 mph (60 f/sec) sees an accident ahead and slams on the...

A:

Q: The price-demand equation and the cost function for the production of a certain product are given, r...

A: Given: p= 15-0.005x C(x) = 2000 + 3x  

Q: 5. (4x'y- 15х? - у )ӑx +x* +3у - х)dy-0

A: Differential Equation is              4x3y-15x2-ydx+x4+3y2-xdy      It is of the form Mdx+Ndy=0     ...

Q: dx Evaluate the given function : Vä(1+væ)

A: Here we have to evaluate the given integral.

Q: lim, 5 f(x) = 2, what is the value of 2 lim, 5[f(x)]° ? О а. 6 O b. 12 c. О с. 8 O d. 16

A: Since you have asked multiple question, we will solve the first question for you as per our guide li...

Q: The area of a square is increasing at a rate of 36 centimeters squared per second. Find the rate of ...

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Q: Which of the following is not true? A 8 (x) dx Su B · 8 (x) ]dx= ƒ (x) dx · dx=k D E) none of the gi...

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Q: Determine the solution to the initial value differential equation 4 y'+ 4 y = 5 e3 x y (0) = 14 y (x...

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Q: What happens if you try to use l'Hospital's Rule to find the limit? lim X → V x- + 3 You cannot appl...

A: Find the limit of the function x/√(x2+3) , x tends to infinity. 

Q: Find the equation of the tangent line to the graph of f(x) = (4x – x2)(4 – x - x2) at x = 1. y =

A:

Q: given

A: We will solve the integration. 

Q: Evaluate J (sin t + 1)-1 dt

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Q: Evaluate the definite integral (5et + 8x)dx using Part 1 of the Fundamental Theorem of Calculus. Ent...

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Q: V3 13) tan 3.

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Q: 3 0 1] 0 2 1 5 2- Find A. A-1 if the matrix A is given by: A =| 0

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Q: Find a formula C(x,y,z) that gives the cost of materials for the closed rectangular box, with dimens...

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Q: ft along a straight, level road decelerates at a constant rate of 22 ft when the brakes are applied....

A: Given query is to find the displacement function.

Q: Solve х — 1 y+2 2 X 15 1- x 5+y 5 6. 2 6. 3.

A: We have to find the value of x and y

Q: 873 4x) da

A: topic - indefinite integral

Q: 12 | g(t) dt = 30 4. 9(7) V3 9(12) = 4 12 g'(x) Evaluate: dr = 16 + (g(x))²

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Q: dy Find for Y da V1 – 23 dy da

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Q: For function, find the point in the graph at which the tangent line has slope 9 Y= -0.025x^2+6x What...

A: The given function is:Y=-0.025x2+6xThe slope is 9

Q: How do you do this in properties of addition.

A: Our Aim is to apply the properies and to solve the fractions given below:-(2) 39+59+49(4) 426+246+33...

Q: dx ? What is the antiderivative of the integrand 2e* A) -2 e + C B *+ C - 2e * + C + C 2 D

A: The given integrand 12exdx

Q: 7. Find : y = (x* = 5«)a0n 5x, (b). y = x2

A: We can find the derivative as below

Q: Find the area enclosed by the x axis and the curve y= 4-x2

A: Find the area enclosed by the x axis and the curve y= 4-x2 

Q: A tank is full of water. Find the work W required to pump the water out of the spout. (Use 9.8 m/s2 ...

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Q: Suppose we need to find an equation of the plane that passes through (1, 2, -2) that contains the li...

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Q: Find the derivative of f(x) = sin (x) and find an equation of the tangent line to the curve f(x) at ...

A: We have to find f'(x) and tangent line.

Q: Find the value of 'n' that satisfies the equation: „C, =, C, the correct value of n)

A: We will find the value of n as shown below

Q: vở tan v4 -dv 5+3 ln cos vt

A:

Q: COS Cos 3x dx CoS

A: I am going to solve the given problem by using some simple calculus to get the required result of th...

Q: The equation of the curve is given as y = 3x + 1

A: topic - slope of curve at a point

Q: x13 – 3x8 dx

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Q: 8. fx,y) = sinx cos y

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Q: The following table gives the values of f(x) as x changes values. What is the lim,, +3 f(x) ? 2.85 2...

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Q: Find dy dx (a) y = (x + 5x) cos 5x, :

A: