Direction: Read then solve the question carefully. Click the letter of the correct answer Find the derivative of the function: f (x) = 4x°cosz. Select one: f' (z) = -42?sinz + 8zcosz O f'(z) = 4x sinz – 8rcosr O f'(x) = -4r°cosz + 8zsinz O f'(z) = 4x°cosz – 8rsinz

Q: 1. The order of the differential equation 5x- d'y aty + 3x + w'y = 0 is

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Q: Find the interval of convergence of (-1)"(x – 4)" Σ Vn2 + 10 n=0 (Use symbolic notation and fraction...

A: Here,          an=limn→∞-1n+1x-4n+1n+12+10-1nx-4nn2+10   =limn→∞ -x-4n2+10n2+2n+11   =limn→∞ x-4n2+1...

Q: dx 5. Evaluate J 9-4x² eax dx 6. Evaluate f 1+e6x dx

A: topic - indefinite integral

Q: 1. When studying graph transformations, we have looked at two basic types: trans- lations and deform...

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Q: Families of Curves: Parabolas with vertex ( h, -3) and it opens to the left

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Q: Solve the differential equation (x – 3y + 2) dx + (3x + 9y – 12) dy = 0

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Q: A graphing calculator is recommended. Let f(x) = x5 – x². (a) Find f'(x). f'(x) = (b) Check to see t...

A: topic - functions and derivatives

Q: Techiefy Co. wants to launch a new product. It is observed that the fixed cost of the new product is...

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Q: (a) Find the velocity of the particle at time t. s'(t) = (b) When is the velocity 0? (Use n as the a...

A: Follow the procedure given below. 

Q: lim log2 ( – &r – 1) 8x – -1) x→-5

A: To evaluate the given limit , substitute  x= -5  in the given expression.

Q: 1 3. lim coS x 14. x-0 5. lim 4x+7

A: Given query is to find indicated limits.

Q: Solve the differential equation (D3 + 7D2 + 19D + 13)y = 0 When x=0, y=0, y'=2, y"=-12, find y ()

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Q: The position of a bird flying along a straight line with s in meters and t in seconds is given by s(...

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Q: 4. Homogeneous Diffe rential Equation: (x* +2.xy – 4y² kdx– (x² – 8.xy – 4y² kdy = Use the substitut...

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Q: Please show your answers to at least 4 decimal places. Suppose that f(x, y) = x°y. The directional d...

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Q: Use the graph to find the following limits. a. lim f(x) b. lim f(x) x-1 x1 a. Find lim f(x) or state...

A: Function and table values are given, we have to find the limits at given points.

Q: Write the following function in terms of its cofunction. sin(79°) When writing your answer, do not i...

A: A function f  is co-function of a function h if f(A) = h(B) when A and B are complementary angles. F...

Q: 3. y'-5y=x²e* – xe*

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Q: (1–sin a)(1+sin a) (1–sin a)(1+sin a) Which expression is equivalent to for all values of a for whic...

A: Solution: 1-sin α1+sin αcos α

Q: The differential equation (2x' - xy - 2y+3 dx- (x²y+2xdy = 0 is exact because OM ON

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Q: In x to show that In a loga x = Use the change of base formula loga x = x In a loga x dx dx In a In ...

A: topic - derivative of logarithmic function

Q: 11.What is the slope of the tangent line to the curve y = 3x? – 5 at poin - O A. -7 О в. -5 O C. -6 ...

A: Differential equation 

Q: Determine whether​ (a) through​ (c) are​ true, and give an explanation or counterexample.

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Q: (A) Find the exact cost of producing the 21st machine. Exact cost of 21st machine = (B) Use marginal...

A: Here n= 21 (No. of units) c(n)=c(21)=total cost of producing 21 machines c(n-1)=c(20)=total cost of ...

Q: 8.What is the derivative with respect to a of f(x) = (5 – x2)²? оА. (5 — а?) (5 — а*) O B. 2(5 – a?)...

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Q: Evaluate the limit. (Use symbolic notation and fractions where needed.) ((-- ) m;) - 3n lim x-37/2 l...

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Q: 2) Sketch the graph of the curve with the polar equation: r=2- sin(20).

A: Polar equation of the curve is r=3-sin(2@)

Q: Suppose the function g statisfies - 32x – 2x2 - 120 < g(x) < r² + 16x + 72. We want to use the Squee...

A: Let f(x)=-32x-2x2-120 h(x)=x2+16x+72 And f(x)≤g(x)≤h(x) We to evaluate g(x) using f(x) and h(x)

Q: If y = x/T, then y' – 1/*. Select one: O True False

A: Given - y = x/π  To show :- y' = 1/π    

Q: x2 2. Find lim x→0 2ª – 1

A: We want to find limit of the function. 

Q: 3. Separation of Variables: x(y+1)dx+ dy = 0

A: Differential equation  Separation of variables

Q: 8. The differential equation (2x-xy-2y+3}dx-(x*y+2xkty = 0 is exact because ÔM ON

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Q: f(x)= 5.738e0.287x By inspecting the graph of an exponential function, find the following. Note: Rou...

A: The given function is: f(x)=5.738e0.287x Using the graph answer the questions about limit values of ...

Q: 2) Evaluate the integral 1 2- -2 XVX -16

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Q: For the cost function C(x)=40+x-1/2x^2 find the marginal average cost when x=2

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Q: Answer the question below: Let h(x, y, z) = ze*y + x² cos(z) cot(y³). The student should find hyzx.

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Q: y The function f(x, y)= (2x* + y* )exp + xy' is homogenous in x and y of degree 2x

A: Follow the procedure given below.

Q: equation

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Q: To Sketch the Graphs of functions using Derivatives. Problem. Consider the function f(x) = 8x - x' w...

A: Given: fx=8x2-x3f'x=16x-3x2 To sketch: The graph of the function using derivatives.

Q: Families of Curves: Parabolas with vertex ( h, -3) and it opens to the left

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Q: 7. lim 42*

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions specify...

Q: Determine whether the integral converges or diverges. Evaluate the integral if it con- verges. d.x x...

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Q: Find the equations of the tangent line and the normal line of the function at the given value of x. ...

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Q: The volume of the solid obtained by rotating the region enclosed by y = x², y = 3x, about the line y...

A: Given: y=x2 ; y=3x   Now find the point of intersection between the curve and line; x2=3xx2-3x=0xx-3...

Q: If h(x) = V5 + 4f(x), where f(1) = 5 and f'(1) = 2, find h'(1). h'(1) =

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Q: | f(t) dt 20z 4, then f (t) dt is If 4x²+21

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Q: Direction: Read and understand the statement before answer. Click "TRUE" if the statement is correct...

A: Limits and functions

Q: Find the volume of liquid needed to fill a sphere of radius R to height . R y

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Q: 1 3 4 -2 3. 2. 3. 3.

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Q: find all of the critical points and local maximums and minimums of each function. (b) f(x) = Vx – 2,

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