_6. What is the derivative of f(x) = (5 – x²)²? а. 2(5- х2) b. 10 – 2x2 C. 4x3 – 20x d.(5 - x?)(5 - х?) 7. What is the equation of the tangent line and the normal line to y = x² – 4x + 2 at (4,2) respectively? a. y = -4x +14 and y = ÷x - 3 b. y = 4x – 14 and y = -x+ 3 C. y = 4x – 14 and y = ÷x +3 d. y = -4x + 14 and y = -x - 3 _8. If y = (2x + 7)², then what is 27 dy, dx dy а. = 2(2x + 7) dy C. = 2 %3D dx dy b. dx dy d. = 4x = 8x + 28 _9. If y = (2x2 – 1), then what is y'? | а. у' — 2x(2х? - 1) + b. y' = 4x(2x² – 1) с. у'%3D 2x(2х? —1)? d. y' = 2x(2x² – 1)2 | 10. If y = v3x – 7, then what is 2? dx dy a. dy 2 %3D С. %3D 2/3x-7 3/3x-7 3x dy b. dx dy d. dx %3D 3/3x-2 V2x-7 11. If y = V6x+1, then what is 9? dx dy = 2(6x + 1) dy С. c. = 2(6x – 1)5 a. %3D | dx dx dy (x² + 6x) dy b. = d. = 3(6x +1)

Q: I FIND THE INDICATED DERIVATIVE IN ITS SIMPLIFIED FORM: (x³-5x)* 1. у3D ; d'y/dx³

A:

Q: Find the general solution of the equations given below: dy i) 4 - y = x² – 3x; dx2

A:

Q: Solve the problem. Show figure or illustrations. 1. A gutter with trapezoidal cross section is to be...

A:

Q: If f and g are continuous function of X, which of the following is true? )dx =D| (x) dx B dx3D 8(x) ...

A: Given :

Q: -7 3 11 →5

A: Given:      A function is a specific type of relation in which each input value has one and only one...

Q: Calculate the volume of a solid enclosed by the following equations z=x2 +1 , x=4, y=9 and the three...

A:

Q: b. dx ans: 2

A: As per bartleby guidelines we only give first question answers. 

Q: 1 [ (2 -y - VE) dy 2 – y – 0. 1 | (2-y (2 – y – V9) dy 0, 2 | (x² – (2 – æ)) dæ - 2 [ (2² – (2 – a))...

A:

Q: Use any method to determine whether the series converge 1 (a) E k + 5k + 1 k=1 This series 1 (b) E; ...

A: We have to find convergence of series

Q: 2 ext 5. g(x) = .x+1.

A:

Q: Sin x 10. y = 2+Cos x 3 2+Cos x Ob. (2+Cos x)? Cos x C. (1+Cos x)2 1+2 Cos x d. (2+Cos x)? Oa. (2+Co...

A:

Q: Test the series below for convergence using the Ratio Test. n² 0.8" n=1 The limit of the ratio test ...

A:

Q: What is the equivalent degree angle measure for the radian angle measure? Select all correct stateme...

A: As we know that; The angle which in radian can be converted into the degree by formula, θd=180°πθr

Q: Question 2 · „] Let a be the vector (2, -3, –1) and b be the vector (6, -2, 3). Find the projection ...

A: Topic = Vector

Q: sin2(x) + sin(x) cos2(x) To evaluate the -dx using basic formula of integration (without using subst...

A:

Q: Evaluate: sin 1 (cos ( ) O sin-(cos () - O sin-(cos ()- O sin (cos ()-- 4. O sin (cos ()) = -

A: All trigonometry ratios  change at π2 and 3π2. In third Quadrant , tangent and cotangent are positiv...

Q: 8. 12. If y = then what is ? x+4 dx dy = 4x(x + 4) dy C. dx -4Vx + 8 dx dy dy = -4(x + 4) d. dx = 8V...

A:

Q: The amount of carbon-14 present in animal bones after t years is given by P(t) = Po e -0.00012097t A...

A:

Q: 13: 3. y = V(4x + 3)3

A:

Q: Compute the given integral. sin xdx %3D +C

A:

Q: Use the chain rule to find the derivative of 4 f(x) = 8V7x + 10x Type your answer without fractional...

A:

Q: dy = ay + b whose dt Write down a differential equation of the form all other solutions diverge from...

A:

Q: 1. A parabola has equation -12x + y? – 24 = 0. Write the equation in standard form.

A: The equation of the parabola is, - 12x + y² - 24 = 0 So, y² = 12x + 24

Q: 2. Suppose that a volcano is erupting. Readings of the rate r(t) at which solid mate- rials are spew...

A:

Q: Sketch the graph of the polynomial function. Make sure your graph shows all intercepts and exhibits ...

A: P(x) = −(2x − 1)(x + 1)(x + 4)

Q: () 2. Use the Squeeze Theorem to evaluate lim r COS

A: Given problem:-

Q: decomposes at a rate proportional to the amount of A present. a) Write an equation that gives the am...

A:

Q: 9. Reduce the following equation to one of the standard forms, classify the surface, then sketch the...

A: General equation of an ellipsoid is given by, (x-p)²/a² +(y-q)²/b² +(z-r)²/c²= 1

Q: Directions: Use the definition of continulty to determine whether fis continuous at e. Identify the ...

A: given is a function.

Q: After school, Shaquille and Reyna need to pick up their basketball uniforms and return to school for...

A:

Q: A soft-drink vendor at a popular beach analyzes his sales records and finds that if he sells x cans ...

A:

Q: Find the tangent line to the curve y = 2x - x? at (2,0)

A: We can find the required answer as below

Q: 4 Let f(x) = 4x + x2 given by y = mx + b for . Then the equation of the tangent line to the graph of...

A: We know that if m is slope and (x1,y1) is point on line the equation of line is given as-  (y - y1 )...

Q: Solve the differential equation 1.) dy = (y²xe^3-3x²y)dx

A: Please see the below picture for detailed solution. 

Q: Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consi...

A: This question is based on solution of Limits of 0/0 indeterminate form solved using L hospitals rule...

Q: This problem concerns the elliptic cone. Consider the equation x²/a² + y²/b² – z²/c² = 0. (a) Descri...

A:

Q: Solve for the value of "C" on the given differential equation below. Let y(1)=1 (9x + y) dx - xdy =0

A:

Q: Find the tangent line to the curve y = 2x - x2 at (2,0)

A: The equation of the curve is given by y = 2x-x2 The point is x0, y0 = 2, 0 Formula Used: The formula...

Q: The daily cost per unit of producing a product by the Ace Company is 30 + 0.2x dollars and the price...

A:

Q: y = V(4x + 3)³

A:

Q: This situation below applies to the next four problems A bacterial colony is cultivated in a petri d...

A:

Q: How fast is the volume V of a rectangular box changing when its length L is 10 ft. and increasing at...

A:

Q: ( 3x?y + ey )dx + ( x3 + xe - 2y)dy=0

A:

Q: %3D +C

A: I am attaching image so that you understand each and every step.

Q: In each of the following problems verify that the given function satisfies the given homogeneous dif...

A:

Q: Determine the sum of the following series. NOTE: Enter the exact, simplified answer as improper frac...

A:

Q: f(t) = e-5t

A:

Q: 3-8 Use the Chain Rule to find dz/dt or dw/dt. 3. z = xy – x'y, x=t + 1, y =t - 1

A: 3) Given:        z=xy3-x2y where x=t2+1 and y=t2-1 substituting x and y values in z     z=t2+1t2-13-...

Q: 1) lim (- sin x

A:

Q: Find the indicated derivatives, using the following information: f(10) = - 3 f'(10) = 1 g(10) = 2 g'...

A: