Find c so that f' (c) = {b) – Aa) b – a in the following ca: x - 3x – 1;a=11 b= 13

Q: Use the chain rule to differentiate f(t)=e^(4t sin(2t))

A: Let us take u=4tsin(2t) and f(t)=y, then we have y=e^u

Q: Find f.  f''(t)=sin t + cos t,    f(0)=2,    f'(0)=4f f(t)= ?

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Q: For f(x) = e+cos(x), calculate f (0) by using the chain rule!

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Q: find f given f (z, y) = e + 2ry 4y at (0,3)

A: Topic- partial differential

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Q: Find the antiderivative F(x) that satisfies the given condition. dF dx = 4e* + 4x²; F(0) = -5

A: Given query is to solve the differential equation.

Q: Find F'(x) given that F(x) = sin (t2) dt

A: Derivative of integration

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Q: Apply the Fundamental Theorem of Calculus to get the following derivative. d In (t² + 1) dt dx 1

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Q: dy from t dx n for y as a function of x, and find two results are consistent by expressing the (a)…

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Q: 1 dx = +C (x+1)² X+1

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Q: Assume that f(x) is a differentiable and invertible function so that f(3) = 4 and f'(3) = .…

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Q: Determine frx and fry for the function below: f (x, y) = x²y + y cos x – e*y In((y) + 7. -

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: f(2) = | : t2 – 1 dt 1+ cos² (t) At what value of ¤| does the local max of f(x) occur?

A: Given that a function f(x) and we find value of x does the local maxima of f(x) occurred. We know…

Q: Find the absolute maxlimum of frr.y)=xy subject to the Coustraint glxy)= x²ty²=/

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Q: f(x) = 9x3 + 4x.   Find the differential of the function.   dy =?

A: Given , y=fx where fx=9x3+4xwe have to find the differential dy

Q: of dx- = 0, then dy |=0. Prove that is a function f is harmonic

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Q: Find the derivate of F(x): z con(2) V64 – t dt .

A: To find derivative of given function.

Q: Given Lve f(t) dt = In(x) cos(x) + sin(3) :L.e- f(t) dt, find f(x). sin(3)

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Q: Verify the final value theorem of f(t) =1+et[sint + cost]. O- 1 1

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Q: Find dz/dr if z as a two variables function in r and y is defined implicitly by y3 + x22 + r sin r…

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Q: dx Show that f - In|ax + b| + C where a # 0. ax+b

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Q: d Use the Fundamental Theorem of Calculus to find the derivative. dx dt 1+ vE

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Q: If F (x) = (t2) dt , then F' (4) = cos 0,

A: DUIS rule is used

Q: Find for F(X,)= Sin xy+ T Y²-x = 0

A: Given query is to find the derivative of the expression.

Q: Use the Quotient Rule to compute the following: d ( t2 +1 at t = -4 %3D dt \ t2 – 1 The derivative…

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Q: ) Find f(t) if f(t) dt : = x sin 6x. A) 0 B) 6 C) n D) 6t

A: According to function,∫0xft dt = x sin 6x

Q: Find of the function f(x,y) = sin(x²y³). əx3

A: The product rule of differentiation : (PQ)'=PQ'+QP' sinx'=cosxcosx'=-sinxxn'=nxn-1 Use the given…

Q: Find the antiderivative of f(x)=cos(3x)

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Q: Fill in the blank. = F(s - a) whereas L eat dt F(s - a) =

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Q: Evaluate the second derivative of mq4.5.png os (bVx³) f(x) = a ln sin(cx2) if a = 21, b = 0.5, and c…

A: Given that, f(x)=alncosbx3sincx2a=21, b=0.5, c=5Substituting the values of a, b and c, we…

Q: Assuming 9x° – 5y - 4xy = 0 defines y as a differentiable function of x, use the theorem dx - to…

A: Given: 9x3-5y2-4xy=0 We have to calculate dydx(1,1) by the given formula.

Q: Q3) For f(x,y) = Sin(x,y) find fryxy at (1,–). %3D

A: Given query is to perform indicated derivative operation.

Q: Find f. (Use C for the constant of the first antiderivative, D for the con f'(t) = Vt - 6 cos(t)

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Q: Suppose that f(x, y) = sin(4x + 6y) is a function of two variables. %3D

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Q: dx = +C (x+1)² X+1

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Q: Find F'(x). 2x F(x) = cos(t*) dt

A: If f(x) is continuous over an interval [a, b], and the function  F(x) = ∫au(x)f(t) dt then F'(x) =…

Q: Using the substitution x = sec 0, dx S: J x2Vx2 _ 1 where x > 1, is equal to

A: We can find the answer as below.

Q: Consider the function f(x) = 9x° + 9x' – 10a? – 4. An antiderivative of f(x) is F(x) = Ax" + Bxm +…

A: Given: fx=9x8+9x7-10x2-4

Q: f(t) dt t sin(rx), -? What is the value of f(5) if

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Q: Consider the function g(x) = 5 S cos t dt – x?. Then g' (x) is

A: Given gx=12∫x4x2costdt  -x2

Q: Find the antiderivative of the function f(x) = - 4 sin (4x) when C = 0. The antiderivative is

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Q: Si f(t) dt = x² – 2x + 1. Find f(x). 79. Suppose that

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Q: Find the value(s) of @ for which y = cos ot satisfies d'y + 16y = 0. di? Enter your answers in…

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Q: Differentiate e w repect to X. expression (x2+y)" (use D fur dy)

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Q: Integrate the following functions f(x)=Ln [sec (x)] [², 3]

A: We will see the graph of secx to judge the value of greatest integer function of secx.

Q: Give a physical interpretation of JT. F.ndS.

A: This expression is of surface integral for calculating the area of the field bounded in the…

Q: Find for the following function: dx 4- y = In2 5- tan-1 V4x - 5

A: Topic : differentiation

Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.