promath The integral of sinxcosx is equal to -(cos2x)/4+C or, (sin2x)/2+C where C is an integration constant. In this post, we will learn how to integrate sinx cosx. The integration formula of sinxcosx is give as follows: Find the integration of sinx cosx Answer: The integration of sinx cosx is (sin2x)/2+C. proof: There are three methods … Read more
The limit of sin2x/sin3x when x approaches 0 is equal to 2/3, that is, limx→0 sin2x/sin3x = 2/3. The limit of sin3x/sin2x when x approaches 0 is equal to 3/2, that is, limx→0 sin3x/sin2x = 3/2. The following formula will be useful to compute the above limits: limx→0 sinx/x = 1 …(∗) Limit of sin2x/sin3x … Read more
The limit of sin2x/x when x→0 is equal to 2 and the limit of sin2x/x when x→∞ is equal to 0. Here we find the limits of sin2x/x when x tends to 0 or ∞. The formulas of the limits of sin2x/x when x→0 or x→∞ is given below: Find limx→0 sin2x/x Answer: The function … Read more
The limit of sin(1/x) as x approaches 0 does not exist, that is, limx→0 sin(1/x) is undefined. The limit formula of sin(1/x) when x→0 is given below: limx→0 sin(1/x) = undefined. Let us learn how to find the limit of sin(1/x) when x approaches 0. Find the Limit of sin(1/x) when x→0 Answer: The function sin(1/x) has no … Read more
The limit of tanx/x as x approaches infinity does not exist, that is, limx→∞ tanx/x is undefined. Here we learn to find the limit of tanx/x when x tends to infinity. The formula of the limit of tanx/x when x approaches ∞ is given by limx→∞ tanx/x = undefined. Below theorem will be useful to prove this … Read more
The limit of tanx/x as x approaches 0 is equal to 1, that is, limx→0 tanx/x = 1. Here we learn to find the limit of x/tanx when x tends 0. The formula of the limit of tanx/x when x→0 is given by limx→0 tanx/x = 1. Proof of limit tanx/x = 1 when x→0 First, we prove … Read more
The value of the limit of x/cosx is equal to 0 when x approaches to 0. Here we will learn how to find the limit of x/cosx when x tends 0. The formula of x/cosx limit as x goes to 0 is given below: limx→0 $\dfrac{x}{\cos x}$ = 0. Proof of limit x/cosx is 0 when … Read more
The general solution of dy/dx=ex+y is equal to ex+ e-y= C, and the solution of dy/dx=ex-y is given by ex – ey= C. Here C denotes an arbitrary constant. Let us learn to solve dy/dx = e^(x+y) and dy/dx = e^(x-y), and find their general solutions. General Solution of dy/dx=ex+y Answer: The general solution of … Read more
The general solution of the differential equation dy/dx=sin(x+y) is given by tan(x+y) – sec(x+y) = x +C where C is an arbitrary constant. Here we will learn how to find the solution of dy/dx=sin(x+y). Let us now solve the differential equation dy/dx=sin(x+y) by the substitution method. General Solution of dy/dx=sin(x+y) Question: Find the general solution … Read more
The general solution of the differential equation dy/dx=x/y is given by y2 = x2 + C where C is an integral constant. Here we will learn how to find the solution of dy/dx=x/y. General Solution of dy/dx=x/y Question: Find the general solution of dy/dx=x/y. Answer: The given differential equation is $\dfrac{dy}{dx}=\dfrac{x}{y}$ Separating the variables x … Read more