Differentiate the function. 7x²-1 3 4x³ +5 y=- y'=0

Q: 1. Calculate the following limits (showing all working): log₂ (n) + 2n no log3 (n) + 3n (a) lim √7n7…

A: We have to find the limits.

Q: What is the final answer here. Please write the letter.

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Q: y (3x² + y²) dx + x(x² + 3y²) dy = 0

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Q: The derivative of f(x)=(3x^1/2+x+x^−4)(5x^−2/3−6x^5/7) is f′(x)=

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Q: Q3. Differentiate f(x,y) = xy² + √x+y² 2 1/1

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Q: Use cylindrical shells to find the volume of the solid generated when the region enclosed by the…

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Q: Determine whether the sequence converges or diverges. If it converges, find the limit. = e-4/√n lim…

A: Given  an = e-4n.

Q: 2. (a) Let==1-i. (i) (ii) Plot the position of on an Argand Diagram. == Express in the form = = ae¹,…

A: solution

Q: lim 1 t-> +→> -∞0 17 + cot = ² +

A: note that cot^-1(- infinty)=0

Q: solve  log10(x+3)-log10 X =1

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Q: 618 x 99 6182

A: using simple multiplication

Q: Q1. Find the exact value of the following Trigonometric function, by identifying the relevant…

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Q: Find the value of the constant m that makes the following function continuous on (-∞0, ∞o). mx - 13…

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Q: Evaluate the derivative of the following function. f(x) = (5x)4x f'(x) = (Simplify your answer.)

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Q: If f(x) = 2x + find f'(1), using the definition of derivative. f' (1) is the limit as x → of the…

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Q: tan 2x lim 3 X-0 X + a 2 X sin bx X = 0

A: Topic:- calculus

Q: If f ( x ) is a linear function, f ( − 2 ) = 0 , and f ( 3 ) = 2 , find an equation for f ( x )

A: We have, f-2 = 0f3 = 2 To determine: The expression of fx if it is a linear function.

Q: f(0) =2, lim f(x) = 2, lim f(x)= lim f(x) = ∞o, lim f(x)= ∞o, and lim f(x) = -00 X4±8 x+37 x-3* X-3+…

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Q: Solve AABC subject to the given conditions, if possible. Round the measures of the angles (in…

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Q: If h(2) = 3 and h'(2) = −8, find. d/dx(h(x)/x) x=2

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Q: Find the derivative of the following functions. Whenever possible, express answer in factored form.…

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Q: Directions: Consider the following function f(x). f(x) = 2x² -x-1 Part 1 - Difference Quotient If h…

A: Given query is to find the derivative using the definition.

Q: Find the equation of the normal line to the curves at the  point of tangency, if given.  1.…

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Q: Let f(x) f'(x) (6x-2)4 (5x2 – 4)6 . Compute f'(x).

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Q: Solve x dy - y dx = 2x³ dx. O y = x^3 - cx O y^3 - x^3 - cx Oy=x^3 + cx O y^3 - x^3 + cx

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Q: let a and b be integers such that 7 divides both a+3b and a-2b. Show that 7 divides a

A: Given 7 divides a+3b and a-2b  Then 7 divides (a+3b)+(a-2b)= a+b  And 7 divides (a+3b)-(a-2b)=5b…

Q: Use integration by parts, together with the techniques of this section, to evaluate the integral.…

A: The given integral is 9ln(x2-x+4).

Q: 3. (y²-2xy +6x) dx- (x²-2xy +2)dy=0

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Q: Let f(x) = 3√√x If g(x) is the graph of f(x) shifted down 4 units and left 3 units, write a formula…

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Q: Write a simpler function that agrees with the given function at all but one point. Then find the…

A: Given, limx→0x4-5x2x2

Q: K Does the graph represent a function that has an inverse? Choose the correct answer below. O No Yes…

A: Here we have to choose the correct option.

Q: Given the following functions, compute the composition (fog)(1). f(z)-3x+6 g(z)-52-7 Simplify your…

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Q: Solve (x5 + 3y) dx - xdy = 0. O 2y = x^5 + cx^3 O 2y = -x^5 + cx^3 O 2x = y^5 + cx^3 O 2x = -y^5 +…

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Q: 7μ Match the point in polar coordinates -2, 4 OA (2.) OB (2, 3) oc(2.- OD(-2,7 X $ to the points A,…

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Q: What is the value of k so thate(x-1)=4e²³x-k? dx

A: givenddxek(kx-1)=4ek2x-k

Q: y''+4y'+5y=  y(0)=0  y'(0)=6

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Q: -3 -1,0 lim g(x) x-2 lim g(x) x→0 g(2) = = =

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Q: 7. y = √√2x² - 4x +3

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Q: 2x-1, At what point/s will the tangent/s to the curve y== 2x+1 be parallel to the line y-4x+3=0?

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Q: original variable. (4)/2√2-1 (a) y³ (b) √ (y² + 1)³ dx dy (c) (d) [²v S Cπ/2 ¹ √1+e-x ex π/4 cotx dx…

A: The objective of the question is evaluate the indefinite integrals .

Q: Use cylindrical shells to find the volume of the solid generated when the shaded region is revolved…

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Q: Find the slope of the line passing through the pair of points or state that the slope is undefined.…

A: Our Aim is to find the slope of the line passing through the pair of points(-4,3) and (2,2). Further…

Q: 2. Find dx/dy if y = √√√1+√x -4√√√√1+√T 4√√√1+√I

A: Given: So,      dydx=1+x'        =121+x1+x'        =121+x·12x        =14x1+x

Q: Determine the equation of the line tangent to the curve y = 4( 4(x+3) y = at the point (5,64).

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

Q: ว | 2 dx น x-9

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Q: Sketch two periods of the graph for the following function. x + π) TU m(x) = 2 csc -X 3

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Q: Find the derivative of the following functions. Whenever possible, express answer in factored form.…

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Q: Use cylindrical shells to find the volume of the solid generated when the shaded region is revolved…

A: The objective of the question is determine volume of the given bounded curve.

Q: 778) Solve for A,B,C,...,H in: (5*9i)=A+jB; (81*8i)=C+iD; 18 (4+4i)=E+iF; ans: 8 (5+91) (2+5i)=G+iH.

A: Topic - Complex numbers We are given, (5*9i)=A+jB (8i*8i)=C+iD ;i8(4+4i)=E+iF ;(5+9i)(2+5i)=G+iH and…

Q: Solve the right triangle for the unknown sides and angles. Round values to 1 decimal place if…

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