A certain bacteria culture is known to grown at a rate proportional to the number of bacteria present. After one hour, 1000 strands of bacteria are seen in the culture. After three hours, this number tripled. Find the number of strands of bacteria originally in the culture.

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Q: Use E-N verification to prove that - →>>> O as n. Vn

A: the answer is in step 2

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A: Understanding of graphs of any function is required to solve this question. Domain of a function is…

Q: > Question 4 Which of the following statements is true? The slope of the tangent line to the curve y…

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Q: 5. Rewrite the expression as an algebraic expression in x. X cos( 1¹ (3)). H≤3 |x|≤3 (a) cos sin

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A: The objective of the question is determine derivative by help of parametric equations.

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A: Given query is to find the solution of the differential equation.

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Q: Evaluate the integral. (Use C for the constant of integration.) in² (7) dt

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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: A certain bacteria culture is known to grown at a rate proportional to the number of bacteria…

A: let   p=amount of bacteria present   thendpdt=growth rate

Q: b) lim 818 c) lim 818 2x³-3x+1 3x4+7x³-2x-1 sin (x+3) X

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Q: y = 8e4x

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Q: 10. The national debt of a South American country t years from now is predicted to be D(t): 65 +9t3…

A: Topic- Application of derivatives We are given, Predicted nationl debt of a South American country t…

Q: Find a. b. C. d. e. f. g. lim x-3 lim x0 lim x → 0+ lim x10 lim x2 f(x) h. f(2) f (x) f (x) f (x)…

A: We need to evaluate the following limit for the given graph of the function a. limx→-3fxb.…

Q: C(x) = 6x³ 30x² + 80x + 1600 where x denotes the number of thousands of televisions produced in a…

A: Given query is to find average cost and marginal average cost.

Q: 2. Find dx/dy if y = √√1+√x 1 -4√√1+√x Option 3 1 4√√√1+√ Option 1 4√x√√1+√x Option 4 -4√√√1+√x…

A: Solve for the dx/dy

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Q: π π €). Calculate E 2 d dxsin (x) (x) eta

A: Topic:- application of integration

Q: General Direction: • Evaluate the limit of the following transcendental functions using TABLE OF…

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Q: ƒ (x) = 3x² + 3, x = 7|

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Q: 4. An object is moved along the line from the point (1, 2, 1) into the origin (distance is in…

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Q: 1. A balloon is released from the ground 30 feet from an observer. The balloon rises directly upward…

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Q: Evaluate the definite integral. e 3 S²₁ dt = dt = 2

A: Evaluate the definite integral  ∫2e3tdt

Q: d Let Arctan² (3e) dx ke*Arctan(f(x)) g(x) Compute kf (0) - g (0) - 3

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Q: The general solution of the Differential Equation (2x-y²)dx-2x(y²-x+y)dy=0 is -xe2Y(x+y2)=C

A: To determine whether the following statement is true or false.The general solution of the…

Q: c) h(t): 5t e (t² + 1)^

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A: Given query is to find the marginal profit at x = 20.

Q: [-1 -10e*+e* dx

A: Topic = Integration

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A: Understanding of function and how to calculate its derivative is required in order to solve this…

Q: Find the area of the region that is enclosed by the card 10+ 10 sin 0. OTE: Enter the exact answer.…

A: Topic:- application of integration

Q: 7. Determine all value(s) of the constant k so that the planes x+2y+3z = 4 and 3x + (k²+2)y+(7-k) z…

A: We need to find values of k.

Q: function of x and y sin (x²z + y²) + 2x³ = y2²+2= If 2 is a differentiable satisfying the equation…

A: sinx2z+πy2+2x3=yz2+2 We have to find ∂z∂x at (1, 3, 0)

Q: Find an integrating factor for the D.E. (2xy³ – 2x ³y ³ − 4xy² + 2x) dx + ( 3x²y² + 4y) dy = 0

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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: (2xy-3x²) dx + (x² + 2y) dy = 0 2

A: Given differential equation:- 2xy-3x2dx+x2+2ydy=0

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

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Q: Integrate. √ ( 7x² + 2/17 - 0²³) 0 3x 4+ dx = 0 +C

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Q: What single deposit of size $X into a fund paying 5% compounded annually is required at t=0 in order…

A: What single deposit of size $X into a fund paying 5% compounded annually is required at t=0 in order…

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

A: Solution

Q: 1. Find the equation of the tangent line to the given curves at point of tangency, if given. 2. y =…

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Q: What is the derivative of f(x)= xe ?

A: To find the derivative.

Q: Problem 1. Determine whether each of the following statements is true or false. If it is true,…

A: (a) The first statement is integration by parts reverse the chain rule.

Q: dy Find when y= dx (a) (c) ax² √bx+c abx² + 4acx (bx + c) √bx + c 3bx² - ax (bx + c) √bx+c :, where…

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Q: Solve the DE dy/dx + (2/x)y = 6x³.

A: Given,            dydx+2xy=6x3To find : Solve the DE.

Q: if f(x)=x^3-16x a) find the domain and range of f b) state approx the open intervals on which f is…

A: For a)

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

A: Given y=3x2+43

Q: P(w)=2w^2 -w +4 /√w *Differentiate the function

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

A: given that,y=x5(1+2x)7 we know that, derivative formulas: (uv)'=uv'+vu' ddx(xn)=nxn-1